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SIR ISAAC NEWTON
SIR ISAAC NEWTON
A BRIEF ACCOUNT OF HIS LIFE AND WORK
FriOFLSbOR OF APPLIED MATHEMATICS, UNIVERSITY OF LEEDS
WITH A PORTRAIT, A
MAP AND IO DIAGRAMS
METHUEN & CO. LTD.
36 ESSEX STREET W.C.
l<irst Pulltshed in 1927
PRINTED IN GREAT BRITAIN
INSCRIBED TO THE MEMORY OF,
THIS brief account of the life and work of Sir
Isaac Newton does not claim to be a critical
biography. The author's object has been to
present the main features of Newton's life and his
chief contributions to knowledge, in a manner that will
be understood by a reader who possesses a very
moderate grounding in the elements of science. Far
too little attention is paid nowadays to the heroes of
science, and it is hoped that the present volume will
help to give to considerable numbers of schoolboys
and schoolgirls, as well as to children of a larger growth,
some insight into the life, personality and achieve-
ments of the greatest man of science England has
Needless to say the author is indebted to many
standard books, especially those by Sir David Brewster,
and to a large number of scattered articles on Newton
and his work. His thanks are due to Mr. Christopher
Turnor of Stoke Rochford for kind permission to use
the marble copy of the famous bust by Roubilliac for
I. THE LINCOLNSHIRE CHILD, 1642-1661 . I
II. THE CAMBRIDGE STUDENT, 1661-1665 . 13
III. THE DAWN OF MATHEMATICAL DISCOVERY,
IV, THE GERM OF UNIVERSAL GRAVITATION,
V. THE ANALYSIS OF LIGHT AND COLOUR,
VI. THE OPTICAL DECADE, 1668-1678 . . 62
VII. THE GRAVITATIONAL DECADE, 1678-1687 8l
VIII. THE " PRINCIPIA," 1687 .... 101
IX. THE TRANSITIONAL DECADE, 1687-1696 . 122
X. THE GUARDIAN OF THE NATION'S COINAGE,
XI. THE DOYEN OF BRITISH SCIENCE, 1703-
XII. THE END, 1727 153
[R ISAAC NEWTON'S FAME
Rev. Barnabas Smith Hannah
Robert Barton Hannah !
.therine * A Daughter * A
.erine Viscount Lymington
on's personal estate.
Newton's family estates at Woolsth
CO +J r& -M
f\ . r*-l -4_> ^
* 5=1 .S
LIST OF ILLUSTRATIONS
SIR ISAAC NEWTON . . . Frontispiece
From a copy of a bust by Koubtlhac, ^n the possession of
Christopher Tumor, Esq., at btoke Rochford
MAP OF NEWTON'S PART OF LINCOLNSHIRE . 6
From a drawing by 4. E. Taylor
1. AREA OF CIRCLE 24
2. KEPLER'S LAWS 40
3. CENTRAL ACCELERATION IN CIRCLE . . 49
4. SPHERICAL ABERRATION 55
5. SPECTRUM 59
6. NEWTON'S RINGS 75
7. FALLING BODY AND ROTATING EARTH , . 85
8. CAUSE OF PRECESSION . . . . 115
9. TIDES Il6
10. PATH OF PERIODIC COMET .... 117
When Newton saw an apple fall, he found
In that slight startle from his contemplation
'Tis said (for I'll not answer above ground
For any sage's creed or calculation)
A mode of proving that the earth turned round
In a most natural whirl, called " gravitation " ;
And this is the sole mortal who could grapple,
Since Adam, with a fall, or with an apple.
Man fell with apples, and with apples rose,
II this be true ; for we must deem the mode
In which Sir Isaac Newton could disclose
Through the then unpaved stars the turnpike road,
A thing to counterbalance human woes :
For ever since immortal man hath glow'd
With all kinds of mechanics, and full soon
Steam-engines will conduct him to the moon.
LORD BYRON : " Don Juan,"
Canto the Tenth, I and II.
SIR ISAAC NEWTON
THE LINCOLNSHIRE CHILD, 1642-1661
At first, the Iniant,
Mewling and pukmg in the nurse's arms.
And then, the whining School-boy, with his satchel,
And shining morning face, creeping like snail
Unwillingly to school. And then, the Lover,
Sighing like furnace, with a woful ballad
Made to his mistress' eye-brow.
WILLIAM SHAKESPEARE : "As You Like It."
IN August, 1642, the sword was drawn in the
armed struggle between King Charles I and his
Parliament. For nearly twenty years the struggle
raged : first the King suffered complete defeat and
Parliament became the supreme arbiter of the destinies
of the nation ; then Parliament's power waned and
became completely subject to the royal will of
Charles II, restored to the powers and prerogatives of
his less fortunate father. While the British people was
in this oscillatory fashion hammering out a form
of political and social life to express concretely its
peculiar genius for ordered and law-abiding freedom,
fully and jealously maintained personal liberty and
inviolability combined with a dignified acceptance
of, and submission to, laws derived by common
consent, there was growing up in its midst a youth
of unparalleled genius, who was to serve humanity
in the scientific sphere, but whose life marked an
2 SIR ISAAC NEWTON
epoch in human development as important and as
significant as any marked by the career of dictator
Detached from the great stream of agitated life,
in the tiny hamlet of Woolsthorpe, in the parish of
Colsterworth in Lincolnshire, about six miles south
of Grantham, and a short distance from the main
north road between London and York, there was born
in the year of strife 1642 a frail child to a young and
widowed mother. This child was Isaac Newton.
When Charles I was executed by his indignant subjects
and the monarchy gave way to a military common-
wealth, this little boy was learning in primitive country
schools the first elements of what was considered to
be a suitable education for a small farmer. When
Cromwell had expelled the Long Parliament and had
been declared Lord High Protector with almost all
regal powers, young Newton went to Grantham in
order to continue his education at the King's School.
Cromwell died when Newton's family had become
convinced that he would never succeed as a farmer
and as manager of the paternal estate in Woolsthorpe.
In 1660, the year of the Stuart restoration and the
complete subjection of the nation's will to the pre-
rogative of its refound royal idol, Newton was pre-
paring for entry upon his studies at Cambridge. The
mind that was to set free the human intellect for
unparalleled progress in the elucidation of the secrets
of nature was approaching maturity, and was about
to embark on a great adventure of discovery that can
safely claim to have no superior, perhaps not even a
rival, in recorded human history.
Our history books are generally too busy to deal
with such phenomena. Time was when historical
records dealt with human heroes rather than with
human movements. But the heroes held up to popular
admiration were of other mould than Newton. Warriors
THE LINCOLNSHIRE CHILD, 1642-1661 3
who had slain, or caused to be slain, their thousands
and their ten thousands, kings and emperors who used
peoples and lands as pawns in their game of power and
empire, royal favourites and jousting nobles all these
and their myrmidons strutted across the page of
history ; and if in the mob represented as gazing with
admiration and envy at the doings of their masters,
could be discovered a Roger Bacon, a Shakespeare,
or a Newton, warming themselves in the patronage of
the great, or struggling with the prejudices and bigotry
of their rulers, this was sufficient condescension and
digression from the main object of the narrative.
Things are indeed different now. The outstanding
personalities of history are mode to fit into a truer
picture of general human progress. Popular move-
ments, national aspirations, industrial development
and social and political ideology now claim the atten-
tion of the historian. Yet it is only natural that men
and women who stood somewhat aside from general
life, and whose activities did not immediately affect
national fortunes, should figure but modestly in the
It is nevertheless a fact that while King and Parlia-
ment were struggling for supremacy, while Cromwell
was with dry piety and powder pursuing the fugitive
remnants of Stuart royalism, while rehabilitated royalty
was revenging itself on its oppressors, there was emerg-
ing a power in the intellectual field of human activity
whose supremacy has been almost unchallenged for
centuries, and bids fair to remain unchallenged for
generations to come.
We all love tales of adventure and stories of derring
do. But need adventure be conceived as restricted to
the sphere of physical strife ? When man had to hew
out for himself a precarious habitation in the primeval
forest, in the face of inhospitable nature and the
rivalry of man and beast, the facing of physical danger
4 SIR ISAAC NEWTON
and the unflinching acceptance of personal hazard
were the supreme virtue, the essential concomitant of
human survival. Now that the races of humanity
are still doomed to struggle with one another for the
possession of the earth, and each race, nation or tribe
conceives it its first duty to defend its claim to the
free and undisturbed enjoyment of the fruits of its
labours, there is virtue in physical prowess and popular
applause for the heroes of national offence and defence.
May we not hope for a better day when adventure will
not connote battle, suffering and death, when human
conquest will have for its aim the widening of the
human empire over the forces of nature, when applause
and admiration will be the reward of intrepid inquiry
into the physical universe in which we live and thought-
ful examination of the moral universe that lives
within us ?
The heroes of this type of adventure, the warriors
to whom fall the spoils of such conquest, are at least
as worthy of our admiration as king and emperor.
Founders of religious systems and movements, prophets
and moral teachers of humanity, philosophers and
scientists, poets and masters of great fiction, have
moulded human life at least as efficaciously as
politicians and favourites. There is as much adventure
in the exercise of the intellectual and spiritual faculties
as in the exercise of the physical faculties, and there is
as much romance in the story of these adventures as
in the narratives of knightly tournaments and martial
Isaac Newton _was born on December 25, 1642.*
* Note on the Calendar : The Gregorian calendar was introduced
in 1582, but was not adopted in Great Britain till 1752. All dates
given in this book are the contemporary English dates, i.e. in
accordance with the Julian, or Old Style, calendar. One exception
will be made. Till 1752 the English new year was on March 25th,
with the result that, e.g., what was called in England January i,
1710, was January 12, 1711 in the Gregorian calendar ! It would
THE LINCOLNSHIRE CHILD, 1642-1661 5
His parentage was undistinguished and of decent
obscurity not poor but by no means wealthy. The
father also Isaac Newton belonged to a family that
had farmed the modest Woolsthorpe estate for several
generations. The mother Hannah Ayscough came
from Market-Overton in Rutlandshire. Later in life
Newton himself had ideas of relationship to some
Scotch Newtons of noble descent. But this nobility
was not apparent at his birth. Isaac Newton's father
died only a few months after the marriage, and several
months before the birth of his only and posthumous
child ; the effects on the physical health of the mother
were sucH that Newton was born prematurely, diminu-
tive in size and sickly in health.
Woolsthorpe Manor House, in which Newton was
born, is still in an excellent state of preservation,
inhabited by people whose family has resided there for
several generations. The room in which the birth
took place is still used as a bedroom, and a tablet over
the mantelpiece records the birth of Newton with the
Nature and Nature's laws lay hid in night,
God said " Let Newton be," and all was light.
The house is pleasantly situated in a very fertile valley,
a few minutes from the Parish Church of Colster-
worth, where the entry of Isaac Newton's baptism on
January i, 1643, is still to be seen.
Isaac lived in this house for many years. At first
he was taken care of by his widowed mother, who also
had a small estate at Sewstern. But a neighbouring
clergyman, Rev. Barnabas Smith of North Witham,
be too confusing to adhere to this practice here, and so our dates will
be in accordance with the Julian calendar, but with the new year at
January ist, so that English January i, 1710 corresponds to
Gregorian January 12, 1710. The difference between the English
and the Gregorian calendars in Newton's lifetime was ten days till
February 28, 1 700, and eleven days after this date.
THE LINCOLNSHIRE CHILD, 1642-1661 7
an old bachelor whom his friends persuaded to marry
at last, married Newton's mother in 1645. Young
Isaac's upbringing was then entrusted to his maternal
grandmother ; he remained at Woolsthorpe while his
mother was with his stepfather in North Witham. He
went to small schools at Stoke and Skillington, and
seems to have enjoyed the care and encouragement of
his maternal uncle, Rev. W. Ayscough of Burton
Coggles. Newton's paternal relations were apparently
but little interested in him till be became famous
and could be of use to them. A paternal uncle lived
in Colsterworth, and it was his grandson, John
Newton, who, as heir-at-law, inherited the estates
Newton had obtained from his father and mother at
Woolsthorpe and at Sewstern. This relative was no
great ornament either to Newton or to humanity.
He sold the estates to Edmund Turnor of Stoke Koch-
ford, whose lineal descendants have been the owners
ofjNewton's birthplace ever since.
(When Isaac reached the age of twelve he had
exhausted the very meagre intellectual resources of
the villages near Woolsthorpe, and in 1655 he was sent
to the King's School, Grantham J He was not expected
to walk the six miles to Grantham every day, and so he
lodged at the house of an apothecary and his wife,
Mr. and Mrs. Clark, next to the George Hotel in the
High Street. The house has disappeared, and its site
is now occupied by an extension of the George Hotel.
King's School, Grantham, still exists in a modernized
form, a modest building in pleasant surroundings.
The Old School, in the form of a small hall, where the
teaching took place in Newton's time, has been well
preserved. Its dimensions are 75! feet by 27 feet,
it has a stage at one end, and is now used for school
assemblies only. The walls and beams bear witness
to the proclivities of schoolboys in all generations
to cut their names wherever possible. Little did
8 SIR ISAAC NEWTON
I. NEWTON, who carved his name on one of the beams
and his initials on another, realize that he was to carve
his name in an indelible manner on the walls of the
temple of fame.
The head master's house is still used as such, but we
need conjure up no romantic scenes of youthful genius
discovered by an admiring and careful mentor. Isaac
Newton did not at first attract any attention at all.
He seemed an ordinary boy, perhaps not very strong,
;and not given to taking any pains to excel in anything.
We have Newton's own authority for stating that he
paid little attention to his studies, while at play he
had not much in common with his schoolfellows.
There was nothing of the infant prodigy about young
Isaac : he possessed dormant powers that needed
It seems absurd to have to say that the awakening
took the form of a kick in the stomach. A boy who
ranked higher than Newton in the academic hierarchy
of the school once caused him considerable pain in this
way. Newton retaliated in lusty manner, fought his
assailant till he would fight no more, and duly rubbed
his nose against the wall of the Grantham Parish
Church which stands by the school to emphasize
the victory of revenge.
Newton was not satisfied with this revenge. His
enemy stood above him at school, and so Newton was
determined to vanquish him here too. He finally
succeeded, and the impulse of the effort carried Newton
on till he reached the proud position of top boy of the
For Newton possessed remarkable reserves of mental
power, and his apparent idleness had been the result
of his preoccupation with matters in which he was
more deeply interested. He was low in school at first,
but when stung to action he soon outstripped all
competitors. He did not play games with the other
THE LINCOLNSHIRE CHILD, 1642-1661 9
boys ; but he did better than play games he invented
new ones. He flew and experimented with kites.
He was silent and thoughtful in disposition, but
naughty enough to attach paper lanterns to the kites
and frighten the simple peasants with the belief that
they saw those dreadful heavenly visitors comets.
He was remarkably good with his hands and could
manipulate tools with great skill, constructing various
mechanical contrivances, including a windmill model,
which was made independent of the winds of heaven
by means of the power supplied by an imprisoned
mouse. Young Newton was an excellent observer of
the motions of the heavenly bodies : he made sundials
which were used for a considerable time one still
exists in the Parish Church at Colsterworth. He drew
well and even wrote some indifferent verse. Newton
was, in a word, a lad of singular ability, doing well
anything that came his way.
As we have seen, Newton was not averse to a
pugilistic encounter when the necessity arose for one,
but in essence he was gentle and not given to rough
play. He seems to have preferred the company of
girl friends to that of boys, and was ever ready to
render them any service of which he was capable.
In 1656 Newton's stepfather died. His mother,
Mrs. Smith, came back to Woolsthorpe, bringing with
her the three children that had been born to her and
the Rev. Barnabas Smith. They were two girls and
a boy : Mary, Benjamin and Hannah Smith. Isaac
must have contracted a great friendship with his step-
brother and two stepsisters : all through his life he
helped them, and he made them his heirs to a very
considerable personal property. A niece, the daughter
of Hannah, became a favourite of Newton's later in
life, and she kept house for him when he lived in
Newton had reached the top of the school, He was
10 SIR ISAAC NEWTON
as well educated as one could expect to be in those
rural surroundings. His mother needed a man to
take charge of the family estates, and what more
natural than to summon Isaac home and invest him
with the authority and the responsibilities of this post
especially as he was the lawful heir to the Wools-
thorpe manor and had been given the Sewstern estate
when his mother married Mr. Smith ? The young
Newton, then in his fifteenth year, came back from
Grantham. No doubt, if he had been interested in
farming and grazing, in buying and selling, Newton
would have made a success of his modest patrimony.
But the truth is that his interest never wandered in
the direction of agricultural pursuits. His work on
and in connexion with the farm was of no real value,
and it soon became clear that what he hungered for
was opportunity for academic study and mechanical
In September, 1658, Oliver Cromwell died. The
heavens sent a violent storm to signalize this event.
Instead of seeing to it that the force of the gale shall
do no damage to the buildings of the farm, to the
produce and the cattle, Isaac spent his time in jumping
with the gale and against the gale hoping in this way
to estimate the force produced by the wind. We can
conceive with what haste Newton's relatives decided
that farming was not the vocation to which he was
born, and how pleased they were to send him back to
the Grantham school and his boy friends, to the
apothecary's house and his girl friends.
There is nothing that canTbe said to characterize
scientific genius as regards matrimony ; some of the
world's greatest mathematicians and astronomers
remained unmarried, others had matrimonial experi-
ences both happy and unhappy, while still others have
not been wanting in the spirit of adventure in this
field. Copernicus was a priestly bachelor. Tycho
THE LINCOLNSHIRE CHILD, 1642-1661 11
Brahe ran off with the proverbial village maiden and
led a married life of alternate storm and calm. Kepler
married twice : he treated the matter of marriage in
a spirit of business-like caution and achieved an
imperfect bliss nevertheless. Newton is credited with
two adventures, both very simple and innocent in
The apothecary's second wife had a daughter by
her first husband, Miss Storey by name. She was
Newton's junior and playfellow, good-looking and
clever. Apparently Newton's pleasure in the company
of girl friends developed into something more mature
in the case of Miss Storey. Butjxjtlj. he and his lady
friend were not rich enough and not poor enough to
do' anything improvident. Newton gave up any ideas
he may have had of married life, and devoted himself
to his studies. He finally went off to Trinity College,
Cambridge, on the advice of his uncle from Burton
Goggles ; Miss Storey stayed in Grantham. Years
later Newton returned to find her married to another
(and to yet another !). To his credit be it said that
Newton retained the memory of his early and tender
regard for Miss Storey during a long life, and extended
to her an ever-ready hand of friendship and help.
Generosity was one of the outstanding features of
Newton's character all through his life, and he was
always making gifts or loans to all who needed such
aid. In a notebook that Newton kept in 1659 we have
ample evidence of his readiness to help where help was
needed. We learn that he spent some money on
" chessemen and dial," while Newton also places on
record the fact that he spent some money on " china
ale," "bottled beere/' "sherbet and reaskes," and
other desiderata of the mortal part of his make-up.
'(Jrom 1658 to 1661 Newton was at the Grantham
school preparing for Cambridge? His local reputation
grew quickly, and when he left school his departure
12 SIR ISAAC NEWTON
was made the occasion of a laudatory address by the
head master. On June 5, 1661, Isaac Newton, then
in his nineteenth year, was admitted to Trinity College,
Cambridge, and embarked upon a career of complete
devotion to science.
THE CAMBRIDGE STUDENT, 1661-1665
And soon the flimsy sums he floored,
And conned the conies thro* and thro*.
S. K. COWAN :
" A Supplemental Examination "
IT has been suggested that the time of reaction and
repose after violent political convulsion is usually
characterized by unparalleled progress in science,
literature and art. The Napoleonic wars were followed
by great developments in all branches of science in
Britain, France and Germany, and the recent European
war has certainly left behind it an interest and an
activity in science which is producing very fast scientific
progress in all civilized nations. Whether we have
here a relationship of cause and effect, whether
humanity in its best minds, being thoroughly ashamed
of its recent bestiality, strives to make amends by
more devout application to the matters of the mind,
we cannot say. It is certainly of interest that the
religious convulsions in the England of the middle of
the sixteenth century were followed by the Elizabethan
period of drama and literature, white the political
disturbances of 1642-1660 were followed by one of the
most brilliant periods of British science, the establish-
ment of the Royal Society and the foundation of the
Royal Observatory at Greenwich.
When Isaac Newton left Woolsthorpe for Cambridge
his local reputation did not imply that he was really
a very learned youth. He knew comparatively little,
U SIR ISAAC NEWTON
especially in mathematics. Other students had done
more than he. This is, in fact, one of the greatest
advantages of going to a university like Cambridge.
He who in his modest home-circle is acclaimed as the
wise and learned man and excites the admiration of
his relatives and neighbours, has to submit to com-
parison with, and the competition of, the best intellects
brought together from all corners of the land. Wools-
thorpe, Colsterworth and Grantham could be proud of
their Isaac, but Cambridge was quite unmoved by.
Newton's arrival. Other students were at least as far
advanced in their studies as he, and young Newton
did not immediately carry off all the prizes within
This was no real disadvantage to Newton. On the
contrary, Newton derived considerable benefit from
his comparatively late development. It is very seldom
that the youthful prodigy carries out the promise of
his early achievements. It is not often that the boy
or girl who is urged on prematurely to advanced studies
reaches real knowledge and understanding of the
fundamental ideas involved in these studies. Nature
does not approve of being hurried. Peaceful bodily
development accompanied by calm mental growth,
with no hot-house and artificial forcing, yield the best
results. The rural surroundings of Newton's early
years, far from the incitement of intense competition
and the rush for cheap reputations, enabled him to
reach healthy mental and physical maturity, untired
by premature exertions.
It was an additional advantage to Newton that he
did not go to the University till well into his nineteenth
year of age. The modern aspect of university life,
which is mainly an avenue to the professions, coupled
with the poverty of most of the students, tends to
send young boys and girls to the universities when
they should still be at school. The university is a
THE CAMBRIDGE STUDENT, 1661-1665 15
place of independent study within the reach of scholars
of outstanding merit and authority. For independent
study an essential desideratum is maturity, culture and
a sense of responsibility. Newton was not hurried :
he came to Cambridge just when his intellect was
arriving at full development.
The vigour of his intellect was soon displayed to his
tutors. On more than one occasion he was found to
have mastered independently treatises that were to
form the topics of extended lecture courses. The
result was that he was released from attending such
courses. He could roam at will in the domains of
knowledge, and he was soon attracted to the studies
with which his name was to become immortally
Kepler's " Optics " is the first book that Newton
read at Trinity, and as we shall see it was in optics that
he made some of his first and epoch-making discoveries.
Attracted by a book on astrology which he picked up
at a fair held near Cambridge, Newton realized his
ignorance of geometry. He therefore bought a copy
of Euclid's " Elements/' It is indeed remarkable that
he was not led to Euclid in a more direct manner, and,
further, that he did not realize the genius of the writer
and the importance of the subject. To his very
practical mind, not given to idle speculation and
reaching conclusions by a marvellous insight and
intuition, Euclid's efforts to prove what appeared to
be self-evident truths suggested that the author was
merely trifling a mistake made so often and so
disastrously in our own generation. Newton suffered
for this mistake. He entered Trinity as a sizar, a
class of student then, and till about a century ago,
required to perform various menial services in return
for his tuition and necessaries of life, or " commons "
as they are still called for Newton's mother was not
rich and he had to use the force of his own intellect
16 SIR ISAAC NEWTON
to raise him in the academic scale. When he competed
for a scholarship in April, 1664, the examiners, while
recommending him for an award, commented on his
poor knowledge of geometry, and Newton was thus
led to reconsider his opinion of Euclid.
Newton's interests were indeed hardly those of a
mathematician as such. (Jlis mind was essentially and
primarily that of an experimenter^ His school days
were spent in a manner that suggested the doer rather
than the thinker, and in the apothecary's house he
acquired a leaning to alchemy and chemical experi-
menting. His main incentive to study was his desire
to understand natural phenomena be they the
motions of the planets and comets, the periodic flow
of the tides, the beautiful colours in the spy-glass
and in soap bubbles, the resistance of the air and the
laws of motion, the properties of substances and the
transmutations of the metals. " Observe the products
of nature in several places, especially in mines . . .
and if you meet with any transmutations out of their
own species into another (as out of iron into copper,
out of any metall into quicksilver, out of one salt into
another, or into an insipid body, etc.), these, above
all, will be worth your noting, being the most luciferous,
and many times lucriferous experiments too in philo-
sophy." So wrote Newton to a friend a few years after
his undergraduate days long before he had forsaken
Cambridge for the London Mint, and gold and silver
had acquired a personal professional interest for him.
Cambridge was not then the home of English mathe-
matics, which flourished rather in Oxford and London.
It was Newton's own genius that gave to Cambridge its
mathematical renown. He studied the algebra of his
time, and the new methods of Rene Descartes, and
at once began to have ideas wherein lay the germs
of the binomial theorem and of the differential
THE CAMBRIDGE STUDENT, 1661-1665 17
The school boy (or girl) of to-day is taught so well
that one often wonders if he can learn at all. ["Good
teaching does not consist in reducing all the ham nuts
to an amorphous powder, and all the hard crusts to
soft pap, which can be swallowed without effort, and
which escape assimilation into the system owing to the
lack of the saliva of mental effort. The learner must
learn and not be merely taught ; the effort must be
his at least as much as the teacher's^ When mathe-
matical teaching is a careful cataloguing of all possible
questions that might be invented by evil-minded
examiners, and literary study has become a careful
cataloguing of insignificant events in the authors'
lives, coupled with pathological investigations into
peculiarities of accidence, syntax and misprints of
successive editions, who will wonder that grown-up
Englishmen do not rush to see Shakespeare's
dramas and do not feel the romance of the binomial
- Yet the binomial theorem is full of romance ; it
throbs with human interest. It is an adventure into
the unknown. Lead the learner on by judicious
encouragement to generalize : (i + #) 2 = i + 2* + # 2 ,
(i + %Y = i + 3* + 3* 2 + * 3 > etc., into (i + x) n =
i + nx + U ^ n """ ' x 2 +...+ nx n ~ l ' + x n , where
x is any number and n is any positive whole number.
He cannot but see in this a conquest of territory visible
to the eye, not mysterious or clothed in the shadows of
night, but the necessary consolidation of empire, the
appropriation of lands without which present posses-
sions are only loosely heldA
But should not the young learner palpitate with
excitement when urged to venture into uncharted
depths and take n to be absolutely anything ? The
series of terms :
18 SIR ISAAC NEWTON
, n(n i) o , n(n i)(n 2) ,
i + nx + - ' x 2 + ^ ' x* + . . .
f 1.2 1.2.3
has no end if n is not a positive whole number : it
goes on and on and on, indefinitely, to infinity. Does
this mean anything ? Can, for instance, the square root
of i + x be as much as a whole and unlimited series
of terms, all following one another in logical and in-
exorable law, and taking us who knows whither ?
We are too civilized in our modern mathematical
teaching. The ruggednesses are smoothed out, and
the polished surface thus produced leads to smooth
and effortless gliding perhaps oftcner to involuntary
skidding. He will be a benefactor of the race who
will contrive to bring back into our schools a sense of
hazard and adventure, the spirit that characterized
those who made and accumulated the knowledge that
is taught there. Then we shall no longer suffer the
boor who claims with pride that he never could under-
stand mathematics, that lessons on algebra and
geometry were occasions for inattentiveness, and that
the binomial theorem is to him merely the topic of
A great discoverer of our own time has said that *,
the truly great discoveries are made in early manhood, ,
that he who has passed beyond his thirtieth year ,
without having contributed such discovery to the sum
of human knowledge, is doomed to go to the grave
without making any great discovery at all. If true,
this thought is a sad one. It is, at any rate, remarkable
that many of the world's most epoch-making discoveries
fell to the lot of youth and not of old age. Lin the case
of Isaac Newton, two grand discoveries which have
rendered his name pre-eminent among all men the
calculus, and universal gravitation were made in germ
Long before he reached his thirtieth year, nay, before
he was twenty-four years of age ; while he discovered
THE CAMBRIDGE STUDENT, 1661-1665 19
the spectrum and the true nature of colour before he
TThe binomial theorem, if not so important as his
omer discoveries, would yet have ensured Newton a
permanent niche in the temple of fame even if he had
done nothing else, and this theorem he constructed
early in 1665, at about the same time as he took the
degree of Bachelor of Arts, when just over twenty-two
Newton's reputation at Trinity was not, however,
commensurate with his powers and with the things he
was doing in his study. We have already seen that
he did not emerge from the scholarship examination
of 1664 without some censure on the score of inadequate
geometrical knowledge. His general behaviour was
not out of the ordinary. He was quite human in his
pursuits and tastes. He visited the beerhouse, played
cards for money and lost, and when he went home
for vacations he brought as presents for his mother
and stepbrother and stepsisters the same childish gifts
that the Cambridge man of to-day carries to doting
We have no information about the order of merit
of the graduates of 1665. Was Newton the outstand-
ing graduate of his year? Was he, perhaps, quite
undistinguished in this examination, without any
obvious signs of his future in fact, immediately
emerging greatness ? We cannot tell. We do know
that he was not elected Fellow at once. He
was busy with the binomial theorem, he invented
the method of fluxions his form of the differential
Calculus he thought about colours and was being led
to experiment with a prism, within a few months of
his becoming B. A. Yet he kept all these things to him-
self. A few notes are extant written in his own hand
andjcontaining references to these and other matters.
ButfNewton was never inclined to making public any
20 SIR ISAAC NEWTON
unfinished or half-baked discoveriesj By the time
that people round him began to suspect that he was
doing things of value, he was well on the way to
becoming the great discoverer and original thinker
that he was soon recognized to be.
THE DAWN OF MATHEMATICAL DISCOVERY, 1665
" Line upon line, line upon line ; here a little and there a little."
Isaiah xxviii, 13
THE Great Plague broke out in 1665 and spread
from London to Cambridge. This put an end
to Newton's regular studies at Trinity, for the
college authorities decided not to face the risk of the
pest overtaking them with all the students in residence.
They therefore dismissed the college on August 8, 1665.
This went on for practically the whole of the time till
December of the same year, for the whole of the second
half of 1666, and for some time in 1667. Newton left
college in 1665, even before the dismissal in August.
These two years were thus a time of intermittent
labour. But we shall soon see that they were by no
We have records in Newton's own hand which date
his pure mathematical progress with considerable
accuracy. Referring to the winter between 1664 and
1665, i.e. about the time of his taking the Bachelor's
degree, Newton says : "At such time I found the
method of Infinite Series ; and in summer, 1665,
being forced from Cambridge by the plague, I com-
puted the area of the Hyperbola at Boothby, in
Lincolnshire, to two and fifty figures by the same
method." In a notebook of Newton's we find an
account of his first discovery of fluxions, written on
May 20, 1665, and another account with applications
22 SIR ISAAC NEWTON
dated November 13, 1665. Now we know that Newton
was away from college during the twelve weeks ending
December 21, 1665. It is therefore clear that he
made excellent use of his enforced exile from Cam-
Modern mathematics is unthinkable without the
calculus. In order to study any natural phenomenon,
it is essential to deal with the rates of change of various
quantities. In heat we want to deal with the rate of
change of temperature, or the rate of heating or
cooling. In dynamics we have to deal with rate of
change of position, or the velocity, with rate of change
of velocity, or the acceleration. In engineering practice
we have to deal with the rate at which work is being
done. In pure mathematics the shape of a curve is
defined by the rate of change of the direction of the
tangent, while the tangent itself indicates the way
in which position on the curve changes in terms of
any two quantities or co-ordinates that define such
The differential calculus is the branch of mathe-
matics that deals with such topics. When once the
suggestion of the fundamental significance of rates has
been made it becomes clear that progress along this
direction is an essential condition of progress in science
at all. Newton realized this, and in his theory of
fluxions, i.e. the rates of flowing or changing quantities,
he discovered the N first practical step in the development
of the calculus.
A geometrical form of the problem is the following :
Given a curve drawn on a sheet of paper, how can we
find its area or the value of any area defined by a
piece of the curve and straight lines ? This is of
fundamental importance, for it is soon seen that if we
plot velocity against time on squared paper, the area
between the curve thus obtained, the time axis, and
two ordinates parallel to the velocity axis, gives the
THE DAWN OF DISCOVERY, 1665 23
distance described. The engineer in his indicator
diagram plots the pressure in the cylinder of his engine
against the position of the piston : the area of the
closed curve obtained during a backward and forward
stroke of the piston gives the work put into the
machinery by the steam or gases in the cylinder.
How can such areas be measured ? We can count
squares and by making the squares small enough we
can, with sufficient labour, obtain useful results. But
such a method is only approximate and empirical
the mathematician would desire, of course, an exact
solution by calculation. What is the exact area of a
circle, of an ellipse, of a piece of a parabola cut off by
any chord, of the space between an hyperbola, an
asymptote and two lines parallel to the other asymp-
tote ? How can they be calculated theoretically ?
The Greeks had faced this problem and applied to
it their incomparable genius. The method of exhaus-
tions was invented for the purpose, and in the hands
of a master like Archimedes yielded useful results.
The area bounded by a closed curve may be considered
to lie between the areas of two polygons, one inscribed
and the other circumscribed to the curve. The greater
the number of sides in the polygons the closer do their
areas approach one another, and the more accurately
therefore can the area of the curve itself be calculated.
Let the numbers of sides be increased indefinitely.
The areas of the two polygons approach one another
indefinitely, giving ultimately the exact area of the
Thus, take a circle. Divide its circumference into,
say, four equal parts at A, B, C, D. Draw the square
ABCD. Draw the tangents at A, B, C, D : they form
another square A'B'C'D'. Then the area of the circle
lies between the; .areas of the two squares. Taking
the radius to be unity, we at once get that the area of
a circle of unit radius lies between 2 and 4. Now
SIR ISAAC NEWTON
divide the circumference into eight equal parts at
A, B, C, D, E, F, G, H : we get a regular octagon
ABCDEFGH inscribed to the circle, while tangents at
these eight points define another regular octagon,
A'B'C'D'E'F'G'H', which surrounds the circle. The
area of the circle lies between the areas of these two
octagons, i.e. between 2-828 and 3-314. Taking
sixteen points we get that the area lies between 3*062
AREA OF CIRCLE
Squares inscribed and circumscribed
Octagons inscribed and circumscribed
and 3- 182. It will be seen how the areas of the polygon
approach one another, and it will be clear how, pro-
ceeding in this way, we can, by means of pure calcula-
tion, reach any degree of accuracy required.
The area sought for is what mathematicians call w.
By means of the method of exhaustions Archimedes
showed that n lies between 3^ and 3yf.
The area of a piece of a parabola cut off by a chord
was also obtained and in this case easily and exactly
by a process based on the same idea. Yet, clever
though the idea may be, and great the mental vigour
of the Greeks, only a few cases could be dealt
THE DAWN OF DISCOVERY, 1665 25
with in this way a really practical process did not
An extension of the area problem is that of finding
the volume enclosed by a surface. The German, John
Kepler, of whose work we shall hear more in the sequel,
was a man of remarkable mathematical genius. Being
in possession of unexpected money one day, he decided
to lay down a stock of wine. The wine was to be
delivered in casks, and naturally the question arose
as to the volume that is contained by a cask. This
volume 'depends on the outline of the cask, for a cask
is approximately defined by the revolution of a curve
round an axis of symmetry, and Kepler set himself
the problem of calculating the volume in terms of the
curve which defines the shape.
Kepler had some, but not complete, success. Whether
he ultimately purchased the wine, and whether its
qualities satisfied his expectations, need not concern
us now. This incident and Kepler's failure served to
stimulate the Italian Cavalierijo put forward in 1635
the epoch-making suggestion,"that an infinite number
of points make a curve, an infinite number of curves
make a surface, an infinite number of surfaces make a
volume. This is not correct logically, and should
read : a curve consists of an infinite number of infinitely
short straight lines, a surface consists of an infinite
number of infinitely narrow strips, a volume consists
of an infinite number of infinitely thin sheets. But
Cavalieri's suggestion is one of the most important in
the history of mathematics, and many useful applica-
tions of his idea were soon obtained, especially by the
Frenchman Fermat, some of whose wonderful theorems
are still puzzling the greatest mathematicians of to-
No general rule was discovered, however, till the
Englishman, John Wallis, of Oxford, found one for
dealing with a whole class of areas, namely, such as
26 SIR ISAAC NEWTON
are defined by curves in which one co-ordinate is
proportional to a power, like the square or cube, of
the other co-ordinate. So long as this power was a
positive whole number no difficulty existed : but when
the power was negative or fractional Wallis had no
means of obtaining the exact result.
Thus, suppose one co-ordinate varies inversely as
the other, as in the curve given when Robert Boyle
plotted the volume against the pressure for a perfect
gas : this curve is called a hyperbola, and this is the
problem referred to by Newton as having engaged his
attention when he fled to Boothby, in Lincolnshire,
because of the plague. The young Newton, then
twenty-two years of age, found the complete law
for dealing with any function involving roots of
complicated expressions, by means of the binomial
But Newton went further. He realized that
Cavalieri's ingenious idea contained the germ of some-
thing far greater. If a curve consists of an infinite
number of infinitely short lines, cannot the length of
the curve be considered as growing by the process of
adding on little line after little line ? If a surface
consists of an infinite number of infinitely narrow
strips, cannot the area of the surface be considered as
growing by the process of adding on narrow strip after
narrow strip ? If a volume consists of an infinite
number of infinitely thin sheets, cannot the volume
be considered as growing by the process of adding on
thin sheet after thin sheet ? Consider a length, area
or volume, not as something fixed and dead, cut and
dried, but as something alive and developing, something
that varies continuously, as flowing water varies from
moment to moment : look at it cinematographically
and not by means of an instantaneous and rigid image
on a dead screen.
This is an idea that has changed the face of
THE DAWN OF DISCOVERY, 1665 27
mathematics. The conception of physical quantities,
including geometrical position, length, etc., as fluent,
the study of rates of flow and of change, opened the
way to unlimited development. The problem of finding
the direction of the tangent at any point of a plane
curve, is at once solved by asking : What is the ratio
of the flows of the two co-ordinates that define the
curve, considered as growing quantities ? In other
words, we differentiate. To find the area of a curve
we have to ask the inverse question : What is the
quantity whose rate of flow divided by the rate of
flow of one co-ordinate gives the other co-ordinate ?
In other words, we integrate. The youth of twenty-two
had not only solved one of the problems of the ages :
he could give an impulse to mathematics leading to
centuries of novel progress and growth. The differen-
tial and integral calculus, the theory of differential
equations, and the vast ramifications of applications
and developments, might have been traced to the
genius of the barely graduated scholar of Trinity.
If Newton's discovery did not immediately set free
the developments that we can now see should have
resulted therefrom, if the discoverer had to face the
possibility of being denied the credit of his own origin-
ality, he had himself to blame. Be it out of modesty,
or out of a sense of extreme cautiousness, Newton kept
the discovery to himself, and denied to the world of
science what was its obvious due, namely, a published
statement of his discovery.
[Newton wrote brief accounts of the method of
fluxions as early as May and November, 1665. He
developed it further in a manuscript dated May 16,
1666, and still further in a tract which he wrote in
October, 1666. . "1$ the last he made twelve applications
of the method, to curvature, concavity and convexity,
maxima and minimq^etc., many of the applications
being new and of importance.^} But the plague raged
28 SIR ISAAC NEWTON
on, Newton worked on and invented the conception
of second fluxions, or what we now call repeated
differentiation, and even his closest mathematical
friends knew nothing of the great events taking place
in this obscure youth's brain.
THE GERM OF UNIVERSAL GRAVITATION, 1666
Sir Isaac Newton was the boy
That climbed the apple tree, sir ;
He then fell down and broke his crown,
And lost his gravity, sir.
J. A. SIDEY : " The Irish Schoolmaster "
THE Great Plague and Newton's enforced
absence from Cambridge meant a serious break,
or succession of breaks, in his work. His
attention had already been directed towards optical
problems, and he was preparing to undertake suitable
experiments for the purpose of elucidating some of the
puzzling things about light and colour, when he had
to give up the work and retire into the country. He
made up for this by special devotion to the pure
mathematical studies : yet Newton's mind was essen-
tially practical and experimental, and subconsciously
searched for natural phenomena and their explana-
Enforced idleness is not always a curse to the deep
thinker, such mental leisure and freedom from immedi-
ate preoccupation with some definite task, are a positive
advantage. The man of science, indeed, often performs
his function most effectively just when, to the unsus-
pecting observer, he is enjoying a mental holiday. The
reception of impressions and their undisturbed incor-
poration in the mental equipment of the scientific
worker finally give rise to the idea that, like the
30 SIR ISAAC NEWTON
prince's kiss, removes the charm that hinders progress,
and substitutes for it a vigorous vitality.
Removed from his college rooms with their prepara-
tions for optical experiments, deprived of the solace
of mathematical treatises which only a college library
could supply, Newton was forced to spend much of
his exile in quiet observation of things round him, in
meditation on problems that occupied the attention
of his generation. The most insistent problem, one
which demanded a solution and which was obviously
ripe for the application to it of some outstanding
intellect, was that of gravitation.
When man emerged from the childlike state in which
things were taken to be what they seemed, he was
forced to the conclusion that the earth upon which he
lived was not the bottom of a sort of pie-dish, with
the sky as a cover. Little by little it was realized that
the earth must be disconnected all round, and in the
last few centuries B.C., and in the first few centuries
A.D., the spherical shape of the earth became the
accepted view of all thinkers. The heavenly bodies,
consisting of the sun and moon and the small specks
of light loosely called stars, were seen to move. The
sun and moon were found to move from east to west
across the sky each day, but the path described varied
from day to day during the year and month respect-
ively, in a more or less regular and periodic manner.
Of the stars, which all appeared to move across the
sky from east to west each night, all, except a few,
moved regularly in exactly the same paths night after
night, although the times of rising and setting of any
particular star varied regularly from night to night.
It was soon observed that this corresponded with the
motion of the sun. The resulting view adopted was
therefore that the heavens as a whole rotate round the
earth from east to west each " day," this day being
called sidereal or stellar. The sun and moon were
UNIVERSAL GRAVITATION, 1666 31
assigned additional motions round the earth from west
to east, the sun going round once in a year, the moon
once in a month.
But there were exceptional stars, to which the name
planets was given. These were unlike the sun and moon
in that they appeared on the sky as tiny specks, but they
imitated the sun and moon in that they had additional
motions round the earth. These planets were Mercury,
Venus, Mars, Jupiter and Saturn. The last three,
namely, Mars, Jupiter and Saturn, went round the
earth from west to east on the whole in periods of
about 2, 12 and 30 years respectively : but com-
plications existed in the form of annual loopings, the
planet stopping in its west to east motion, then actually
moving back, i.e. east to west, then stopping again
and resuming its west to east motion. Mercury and
Venus executed motions that were at first not at all
clear to visualize. They seemed to hug the sun in a
peculiar manner, appearing sometimes to the east of
the sun as evening stars, then becoming invisible and
reappearing on the west of the sun as morning stars,
and so on indefinitely. It was finally accepted that
Mercury and Venus also go round the earth, but unlike
the other or outer planets, they both take a year to
go round the earth, and execute loops in other and
shorter periods, 88 days per period in the case of
Mercury, 225 days per period in the case of Venus.
There thus arose the famous Ptolemaic system of
the universe in which the earth was taken as spherical
and absolutely fixed at the centre of the universe, the
whole universe rotating round the earth once a day,
and the moon, Mercury, Venus, the sun, Mars, Jupiter
and Saturn going round the earth once each month,
year, year, year, 2 years, 12 years, 30 years respectively,
with no loop in the moon's motion, an 88-day loop in
Mercury's motion, a 225-day loop in the motion of Venus,
no loop in the sun's motion, and annual loops in the
32 SIR ISAAC NEWTON
motions of Mars, Jupiter and Saturn. The circuit and
loop were in each case represented as mption on a
deferent and epicycle, the planet moving on the
circumference of the epicycle whose centre moved on
the circumference of the deferent.
The Ptolemaic system, first given to the world in
the second century A.D., soon became accepted doctrine.
When European nations sank into semi-barbarism at
least, as far as the arts and sciences were concerned
in the early Middle Ages, the Arabs and the Jews kept
the Ptolemaic astronomy alive, just as they kept other
products of Greek science alive, and even made some
significant additions. Such additions were essential
since, after all, the only test that can be applied to a
scientific theory is comparison with fact. If in political
controversy facts are not seldom modified so as to
make them fit more comfortably into some particular
theory, it is nevertheless true that in science facts
are supreme. A theory is indeed a summing up of a
number of facts. If I say that two volumes of hyd'rb-
gen explode with one volume of oxygen to produce
two volumes of water vapour at the same temperature
and pressure, then I do not mean that some tribunal
has decreed that hydrogen and oxygen must do this
and refuse at their peril. What I mean is that when-
ever the experiment has been tried it has been found
to yield this result. We therefore, with that faith in
the reasonableness of nature which we call causality,
assume perhaps with pathetic if unconscious humour
in the eyes of a superior intelligence that the same
result obtains in all cases, even when not observed by
us, and will obtain in future. This is a theory about
water. Let but one case arise in which this result is not
obtained, and the theory begins to wobble, and unless
the deviation from theory is adequately accounted for,
the theory must give way to a more adequate one.
Ptolemy's theory was not only qualitative, it had
UNIVERSAL GRAVITATION, 1666 33
to be quantitative too. With their marvellous
sense foitphilosophic values the ancient Greeks realized
that a theory must be quantitative, that it is not
sufficient to assert vaguely that the moon goes
round the earth, but we must state exactly what the
path is and how fast the motion is at any moment.
Now the Greeks knew practically nothing about the
science of dynamics (the other contemporary nations
knew next to nothing of anything). There are several
reasons why this should have been the case, as we
shall soon see. The Greeks therefore had to make
some basic assumptions, which we now know to have
been without justification. They divided matter into
earthly and celestial. Earthly matter was subjected
to the earth's influence and moved up and down,
perpendicular to the earth's surface. Heavenly matter,
on the other hand, was free of this materialistic
influence, and so moved in a perfect manner, i.e. on
circles round the earth with constant speeds along
To our modern ears such statements sound bizarre.
Why should uniform motion on the circumference of
a circle be the perfection of motion ? Why should
some matter be called celestial and granted the privi-
lege of this perfect motion ? The foundations of
dynamics have been changed since then, and Newton
had a great share in producing the change. Yet it
must be remembered that even to-day there is in at
least some of us a lurking belief that the heavenly
bodies are somehow heavenly, while matter on our
earth is after all only earthly. People still exist who
dub as materialistic the astronomy that considers all
matter in the universe as of the same kind as the
matter of and on our earth, in spite of the fact that
the unique position of the earth in the economy of the
universe is no longer believed in even by such muddled
34 SIR ISAAC NEWTON
According to the Ptolemaic system then, all the
heavenly bodies moved on circles with uniform motions.
The so-called fixed stars called for no further comment.
In the case of the planets Mercury, Venus, Mars,
Jupiter and Saturn, deferents and epicycles had to be
introduced, but the centre of the epicycle moved
uniformly round the deferent and the planet moved
uniformly on the epicycle. For the sun and moon no
epicycles seemed necessary.
But the facts began to be troublesome. When the
position of a planet at any moment was calculated
from this theory and compared with the observed
position in the sky, the agreement was often bad, in
fact very bad, and this applied to the sun and moon
too. Modifications had to be introduced. The centre
of the sun's annual path was taken to be different
from the centre of the earth, and when this did not
suffice the uniform motion of the sun on its circle was
taken with reference to angular motion as seen from
some third point. And so on : in the case of each
body such and similar complications were introduced.
And all through the Middle Ages these complications
accumulated. The instinct that underlay this process
was excellent fact is supreme and theory must be
modified to suit the facts. But clearly something was
wrong somewhere. For there is another instinct in us
which sees beauty and truth in simplicity, and when
a scientific king scoffed at the astronomers by saying
that had he been present at creation he could have
given some good advice, he was merely giving expres-
sion to the healthy desire of science to arrive at simple
truth which needs no frills and furbelows to make her
Views other than Ptolemy's had been expressed in
ancient times, and suggestions had been made that
possibly things are quite different. Must we assume
the earth to be fixed, and at the centre of the universe ?
UNIVERSAL GRAVITATION, 1666 35
Perhaps the earth rotates. Perhaps the earth's centre
moves. Perhaps the earth is a body moving round
another body, and perhaps this other body is the sun.
Such views were, however, effectively silenced, parti-
cularly during the later Middle Ages, when Ptolemaic
astronomy finally conquered Europe, and became
invested with supreme authority. Authority was the
keynote of those days. Truth existed somewhere, and
the search for truth meant the search for hidden
meanings in the pronouncements of authority, be it in
the Bible, in Aristotle, or in any other accepted and
A spherical earth was indeed sufficient departure from
primitive and naive belief. To envisage humanity as
standing all round a globe with heads pointing out-
wards in all directions already did violence to a
psychology that saw a physical and intellectual
anchorage in a flat and stably-fixed earth. To deny
the fixity of the earth and to make it wander about
in space while gyrating on its axis meant deranging
still further the mental equilibrium of humanity.
New ideas were not welcomed in those days. The
initiation of a scientific revolution nowadays meets
with wide approval revolution is often met with open
arms for its own sake, and accorded a publicity worthy
of better causes. But in the later Middle Ages scientific
originality brought with it a publicity of an undesirable
kind and notoriety of an unpleasant character. We
can therefore appreciate all the more the intellectual
compulsion that forced Nicolas Copernicus to discard
at least a part of the Ptolemaic system.
Everything pointed in the direction of change. If
the sun is one of the planets going round the earth,
why should the epicycle periods in the case of Mars,
Jupiter and Saturn, and the deferent periods in the
case of Mercury and Venus, be exactly the same as the
period of the sun's motion round the earth, namely, a
86 SIR ISAAC NEWTON
year ? Why are the sun and moon exceptional in not
having loops in their paths ? The planets are very
far away from us : the nearest to us, the moon, has a
distance from us sixty times as great as the earth's
radius (it is true that in Copernicus' time the moon's
distance was taken to be somewhat less, but this does
not diminish the force of the argument) ; the sun is still
further from us, the planets are still more distant, and
the fixed stars are even further off. Does all this
universe (and Copernicus did not, in fact, have any
adequate idea of how vast the universe really is) re-
volve round the earth, and as fast as once in a day of
twenty-four hours ?
We cannot believe direct and untutored visual
impressions. We must use our brains and reason out
sensible conclusions. Things are not what they seem.
Our impressions of motion are relative : the man on
the clift sees the ship depart from the shore, while the
man on board the ship sees the shore and cliff depart
from him. Copernicus was forced to the grand
conclusion that the earth is not fixed and is not at
the centre of the universe. The earth rotates on her
axis once a day : this explains in rational manner the
apparent rotation of the whole universe round the
earth every day. The earth revolves round the sun
once a year : this explains in rational manner the
loops in the paths of Mars, Jupiter and Saturn, which
also go round the sun in circles greater than the earth's
orbit, and the peculiar hugging of the sun by Mercury
and Venus, which go round the sun in circles smaller
than the earth's orbit. The marvel of the exact year
period of the epicyclic motion in the case of the outer
planets, and the exact year period of the deferent
motion in the case of the inner planets, now dis-
A beautifully simple solar system emerges, slim
in conception and unencumbered by deferent and
UNIVERSAL GRAVITATION, 1666 to
epicycle. The sun is exceptional and has no looping
motion, because it is indeed the exceptional member
of the system, the monarch reigqing at its centre, the
hub of the universe : the moon Has no looping motion,
because it is also exceptional it is not a planet at all.
The moon is a satellite, attached and subservient to
the earth, going round the earth and playing only a
secondary role in the solar system the Copernican
Public attention was drawn to this view only after
the death of Copernicus in 1543. A howl of indignation
went up from established authority, but Copernicus
was fortunate in being dead, for all that could be done
to him was to execrate his name and forbid the reading
of his book and the dissemination of his .system. It is
generally believed that the Catholic church was mainly
responsible for this. It is not so : all constituted
authority, Catholic and Protestant, religious and
secular, opposed the new astronomy. The opposition,
in fact, was the slothful indignation of human intellec-
tual inertia, that refused to be moved from its moorings,
and that feared to give up the fixed earth and wander
about with bearings lost in a bewildering universe.
Why, even the very week was in danger : for were not
the seven days of the week, sanctified by Biblical
command, associated with the seven planets of pre-
Ptolemaic astronomy ?
Yet Qopernicus triumphed. After Galileo's dis-
covery of the satellites of Jupiter, the phases of Venus,
the discs of Mars, Jupiter and Saturn, no other view
than that of Copernicus could survive. By the middle
of the seventeenth century no enlightened person who
was free from papal and other backward religious
authority could do other than accept the Copernican
It is the irony of human progress that the revolu-
tionary very soon finds himself outdistanced by his
88 SIR ISAAC NEWTON
disciples. Copernicus' system was a tremendous
advance on the old system, but his dynamical know-
ledge was hardly, if at all, in advance of Ptolemy's.
In abolishing the central position and fixity of the
earth, Copernicus paved the way for the abolition of
Greek ideas of motion based upon earthly and celestial
types of matter, and caused the emergence of the
problem of dynamics the why and the wherefore of
motion and changes of motion with peculiar insistence.
But he could not liberate himself from the perfect, i.e.
uniform circular, motions of the planets, including the
earth, round the sun, and of the moon round the earth.
In Copernicus' great work, " De Revolutionibus
Orbium Coelestium" (1543), epicycles and excentrics
are still piled upon one another : one marvels, in fact,
at Copernicus' genius all the more in that he did
manage to convert the earth into a rotating planet
revolving round the sun, while he was himself yet
subjected to the bondage of Greek dynamics, and had
to use epicycles for other purposes.
John Kepler was the man who actually liberated
himself and mankind from the effects of Greek dyna-
mical ideas in relation to astronomy ; he took the step
that was necessary to complete Copernicus' work.
Basing himself on the careful observations of Mars
made by his teacher, Tycho Brahe the greatest
instrumentalist and observer of the Middle Ages and
also by himself, he discovered the true paths of the
Kepler realized at the outset of his work that circular
motions had to go. He searched for the true paths of
the planets. He had no clue except the rather doubtful
one that somehow the ancient Greeks had, for purely
theoretical reasons, studied with considerable care the
curves known as conic sections, the curves obtained
when a circular cone is cut by a plane. This study
had been part of mathematical education even since,
UNIVERSAL GRAVITATION, 1666 89
and Kepler thought of trying whether the paths of
Mars and the earth round the sun could be taken to
be conies and give results in accordance with Tycho
Brahe's observations. The conies had to be closed,
i.e. ellipses. It was a sheer guess, the leap forward of
the man of pre-eminent genius.
If the earth and Mars go round the sun in ellipses,
what is the relation of each ellipse to the sun ? An
ellipse has three pre-eminent points inside it the
centre and the two foci : the latter are the points used
for drawing an ellipse quickly, since, if a string lies on
a board with its end-points fixed, and is stretched by
means of a pencil which runs round it, then the pencil
describes an ellipse of which the end-points of the
string are the two foci. We may guess that if the
path of a planet is an ellipse, then either the centre of
the ellipse or one of its foci will be at the centre of
the sun. Which is the correct point ?
If we have the correct point, the next question is :
How does the planet move round the elliptic path ?
What is its speed at any point of the path ? If Kepler
had possessed any true dynamical knowledge then he
would have found out the law of this speed very easily
he might have forestalled Newton. But dynamical
progress came too late for him. He had to discover
the truth by sheer heavy arithmetical calculation. It
was a mighty task that would have been beyond the
powers of any other man. Kepler held out. His
calculations were to him the romantic quest for a
celestial gift he pursued them with the ardour and
devotion of a fanatic. He laboured for a decade,
without even the help of the logarithmic tables that
were then being invented and calculated by Napier
and Briggs in Britain. He tried hypothesis after
hypothesis finally he triumphed. He discovered the
laws that go by his name Kepler's laws of planetary
motion (1609) :
SIR ISAAC NEWTON
I. Every planet moves on an ellipse with a focus at
the centre of the sun ;
II. The line joining the centre of the sun to the t
centre of the planet sweeps out equal areas in equal
3i A Aphelion
Simultaneous positions of two planets in their orbits. AP/A'P* = 1*84, so that
ratio of periodic times is i 84" /a = 2.5. Circles represent oppositions of the two
planets. Squares represent conjunctions of the two planets.
The first law is intelligible, but what does the second
law mean ? Kepler did not know. He was the
discoverer of the truth but not of the significance of
this truth. It was a great achievement to discover
the true paths of the planets. It was the coping-stone
to the Copernican system, the completion of the
UNIVERSAL GRAVITATION, 1666 41
revolution initiated by Copernicus, which did away
once and for all with the deferents and epicycles,
excentrics and equants of mediaeval astronomy.
Kepler put into the Copernican system the spirit of
modernity. How Copernicus would have rejoiced to
learn the truth from his posthumous disciple !
Kepler had yet another problem to solve the
problem of his youth. Was there any relationship
between the distances of the planets from the sun ?
He had foolish speculations at first, but he finally hit
upon a wonderful and simple truth. His third law
III. The square of the time taken by a planet to
describe its path completely once round the sun is
proportional to the cube of its mean distance from
is indeed a peculiar law, savouring of the mysterious
that Kepler loved so well.
A new problem now began to emerge. Whereas the
question so far had been : How do the planets move ?
the question now became : Why do the planets move
in the manner discovered by Copernicus and Kepler ?
The motions of the planets had been found : they had
to be explained. This became particularly urgent
when Kepler published his laws. One might perhaps
ascribe uniform circular motion to celestial matter and
flatter oneself that one is doing something sensible
but it becomes difficult to do this conscientiously with
elliptic motion round a focus in which the " radius
vector " sweeps out areas proportional to the time.
Planets may be deities and as such choose to march
sedately and majestically in perfect circles with
unvarying speeds impervious to all influences tend-
ing to hurry or to delay them. But it is difficult to
envisage a planetary deity at the end of a sort of
municipal rolling broom, that obeys trade-union rules
42 SIR ISAAC NEWTON
and sweeps out so much area per day no more and
Kepler himself tried to explain the motions that he
had unravelled. He failed. A sort of gravitational
influence of the sun on the planets was suggested by
him, even the law of the inverse square of the distance
suggested itself to him and to others in France, in
Italy and in England but to no effect. A dynamical
explanation of planetary motions was out of the
question so long as the foundations of dynamics had
not been discovered.
It is for this reason that the Vortex Theory of Descartes
enjoyed such a vogue. To explain with considerable
plausibility the whirling of the planets round the sun,
and of the satellites round the planets, one need only
observe the way in which whirlpools in water carry
with them the bodies caught by them, forming minor
whirlpools or eddies, which exert local influences of
the same kind. Descartes therefore postulated vortices
in an ocean of " ether," filling up the whole of the
space occupied by the solar system.
Quantitatively, Descartes' theory breaks down, but
it held the field because there was no competitor.
Vague ideas about gravitation could not dethrone a
theory supported by the authority of this great
philosopher and mathematician. Views based upon
sound dynamical principles alone could rout the vortex
Fortunately, the dynamical principles were soon
available. Galileo's great astronomical discoveries
have had the effect of eclipsing somewhat the lustre
of his fame in the history of dynamics. If astronomy
suffered from the arrogance of self-constituted authority,
it had at least one advantage observation of the skies
was encouraged both by nature and by man. A man
is indeed no higher than the beasts of the field if he
is not attracted by the aspect of the heavens, especially
UNIVERSAL GRAVITATION, 1666 43
in the clear skies of Italy. The observation of the
heavens was also encouraged (from mixed motives) by
kings and princes. When man believed that the
heavenly bodies shone for his benefit and so as to
enable him to foretell the future of his petty affairs,
detailed study of these bodies was an essential consti-
tuent of government and statesmanship. The emperor
Rudolf may have meant astrology when he installed
Tycho Brahe in Prag Tycho Brahe could get on with
his astronomy nevertheless. Astronomical discovery
was thus in a sense inevitable. In the case of dynamics,
however, if nature did occasionally suggest feebly :
" Observe the motions of bodies and the causes of
these motions," man did not respond to the invitation.
Why observe the motions of bodies when Aristotle
has told us all about them already ? This would
only tend to encourage scepticism and to undermine
And dynamical laws required very exceptional
powers of observation and of intuition for their
unravelling. It is difficult nowadays to measure
accurately the velocity with which a body is moving
at any moment in the early seventeenth century it
was quite impossible. It was even difficult to observe
accurately the position of a falling body from second
to second, in an age when the measurement of time
did not yet enjoy the help of modern clocks and
chronographs. Further, motions are liable to all kinds
of disturbances air resistance, friction, surface irregu-
larities, and so on. Finally, where was the mathe-
matical machinery for dealing with motions and
changes of motion before Newton invented it in his
method of fluxions ?
It was Galileo who ventured to dispute the authority
of Aristotle in the dynamical field. He experimented
and he discovered that the rate of fall of a body near
the earth does not depend upon the weight of the
44 SIR ISAAC NEWTON
body if this weight be sufficient in relation to the
size of the body to make the effect of air-resistance
negligible. Bodies falling from the same level reach
the ground after the same interval of time. Finally
he discovered that a falling body moves in a re-
markable manner its speed increases with the time
in a perfectly regular manner, it is accelerated
The regular increase in the speed of a falling body
is of course due to the pull of the earth on the body,
what we call the body's weight. It must follow
therefore that a steady pull produces a steady increase
of velocity a new and a revolutionary idea. To the
forerunners, and even to the contemporaries of Galileo,
motion connoted force wherever motion existed force
had to exist to explain it. In Galileo's mind a new
idea began to dawn : not motion connotes force, but
change of motion connotes force. A body moving
under no force enjoys constant speed in constant
direction : let a force act upon it and its speed or its
direction or both will vary. Galileo could not prove
this directly, since a body moving under no force
cannot be realized. But the man of genius sees
further than the limited range of the available experi-
ence he makes the leap that carries the human soul
forward on the wings of discovery, and Galileo was a
man of exceptional genius.
Here was the beginning of true dynamics. The
ancient belief was no force, no motion. The modern
view is no force, no change of motion, i.e. no accelera-
tion. Need we wonder at the circumstance that this
truth lay so long undiscovered ? Think of the ox-cart
in which Homer's father went to market think of the
hardships of locomotion in those days, and right down
nearly to our own generation. The only smooth road
known then was the sea and the sea gave the sea-
farers of those days sufficient to think about to divert
UNIVERSAL GRAVITATION, 1666 45
their minds from dynamical speculations. It needed
a mighty intellectual effort of scientific abstraction to
dissociate locomotion from the jolting and the sense
of effort that accompanied it, and to see in the ideal
smooth and unvarying motion the raw matter, so to
speak, of dynamics.
The discovery of the true laws of motion in 1637
set the road free for progress in the dynamics of
astronomy. Men of the greatest eminence sought for
the solution of the problem of the planets. Robert
Hooke in England a man of considerable, if erratic
and unstable, genius, the discoverer of the ut tensio
sic vis of elasticity speculated on this problem, and
even announced that no doubt he could solve it by
combining the conception of gravitation with the dyna-
mics of Galileo if only he could hit upon the correct
law of force to attribute to the sun's gravitation, the
exact way in which this force depended upon the
distance of a planet from the sun. It was the youthful
Newton, meditating in the exile of his Lincolnshire
garden, who approached the problem with a direct
frontal attack, remarkable and historic even in its
(Tradition relates that one day in 1666 Newton was
sitting in his garden at Woolsthorpe, when he saw an
apple fall from a tree : this suggested gravitation to
him, that the fall of the apple was due to the earth's
pull, and hence arose his discovery of the law of gravi-
tation] There is a rival tradition which makes Newton
observe the fall of the apple through a window on the
first floor of the manor house. The apple tree itself
became the object of general interest and historic sig-
nificance, and it was kept standing till blown down by
a gale in 1820. A chair made from the wood of this tree
is to be seen at Stoke Rochford. Descendants of the
tree are said to be thriving to this day ; but all efforts
to make the descendants take root in their original
46 SIR ISAAC NEWTON
and ancestral garden at Woolsthorpe have met with
no success !
Popular imagination clings to this apple incident
yet j it is clear that Newton was not the first man ta
see an apple fall, or to ask himself why an apple falls.
Newton did not discover that the earth pulls the apple
the earth's gravitation was common knowledge in
ancient times, and Galileo had, when Newton was still
unborn, discovered all about the fall of an apple or
of any other body free to give way to the earth's pull.
The fall of the apple if it was really responsible for
initiating in Newton's mind the train of thought that
culminated in the discovery of the law of gravitation
did it in the following manner, if one may venture
to put into feeble words the flash of Newton's genius :
" Why do the planets go round the sun ? Why do
they not move in straight lines ? Evidently there is
a force pulling them out of the straight-line path at
every moment, and clearly this force is due to the sun.
The moon goes round the earth and does not go off in
a straight line. This must be due to the earth. Ah !
An apple has just fallen to the ground : the earth has
pulled it down. How far up does the earth's influence
extend ? We know that no matter how high up we
go to the summits of the highest mountains this
influence exists without obvious weakening. Does the
earth's gravitation extend to any distance, no matter
how great perhaps even as far as the moon ? Can >
this be the force that compels the moon to accompany/
the earth, to travel round and round the earth indefi-l
nitely as the earth travels round the sun ? \
" Yes, this is a pretty theory : can it be proved ?
Can it be shown that the pull required to explain the
moon's motion is just that afforded by the earth's
gravitation ? Any attempt at such proof must postu-
late some law according to which the gravitative pull
of the earth varies with the distance from the earth ;
UNIVERSAL GRAVITATION, 1666 47
for clearly we cannot suppose this pull to be the same
for all distances, even to the ends of the universe. It
must diminish as the distance increases. What is the
law of this diminution ? Suppose that one body is
twice as far from the earth's centre as another : what
is the relationship between the pulls exerted by the
earth on these bodies ? "
The most important step in the solution of any
natural problem is the formulation of the problem itself.
Newton formulated his problem in masterly manner
it only remained to attack the solution. Two steps
had to be taken. The first was to determine how a
gravitational pull would vary with distance from the
gravitating body. The second was to see whether the
earth's pull on the falling apple could also account for
the motion of the moon.
How should a gravitational pull vary with distance ?
A very simple consideration at once suggests a solution.
Suppose that from a point O there is a gravitational
influence in all directions. Take two spheres with
centres at O, one having double the radius of the other.
The same gravitational influence is spread out over
the surfaces of the two spheres : but the sphere of
double radius has a surface area four times that of the
smaller sphere. It follows that the gravitational pull
at a point on the larger, double, sphere must be one-
quarter of the pull at a point on the smaller sphere.
This is at once generalized into the inverse square law,
namely, that the pull exerted at any point is inversely
proportional to the square of the distance of this point
from the gravitating body.
Such considerations would run through Newton's
mind ; but Newton was remarkably realistic in his
outlook upon nature and her problems. An ounce of
observational or experimental proof was worth to
him more than a pound of theoretical argumentation.
This characteristic accompanied him all through his
48 SIR ISAAC NEWTON
long career of scientific activity. Newton looked for
observational justification of the inverse square law
and the third law of Kepler, discovered nearly half a
century before, and quite ununderstood all that time,
gave him the proof he desired.
The planets move on ellipses : but these ellipses are
nearly circles this was indeed why circular motions
were insisted upon till Kepler's success in emancipating
us from them. Except for the planet Mercury, the
planetary paths are so nearly circles that, for a rough
calculation, we can ignore their ellipticities and assume
them to be circles with their centres at the centre of
the sun. Further, the motions on the paths are variable
yet the variations are really very small and we can
for a first approximation imagine the planets to describe
circular paths with constant speeds.
It needed the mental courage of a Newton to thrust
himself back in this way into the primitive views of
Greek astronomy uniform circular motions. Newton
was not yet mathematically ripe to solve the problem
of the planets in their fullness. With characteristic
clarity of vision he pounced upon the essential and
discarded the inessential. He felt that what he needed
could be obtained by such approximate argumenta-
Now if a body moves on a circle with constant
speed there must be a force producing the continuous
change in direction of the motion ; this follows from
Galileo's dynamical discoveries. Every schooboy who
has done a little mechanics knows that the force
required is the mass of the moving body multiplied by
the product of the speed into the rate at which the
direction of motion is rotating. This means that for
radius r and angular velocity n the force per unit mass
of the moving body must be the speed rn into the rate
at which the direction of motion rotates, namely, n.
Hence the force per unit mass must be n*r.
UNIVERSAL GRAVITATION, 1666 49
But Kepler's third law states that the squares of
times taken by the planets to travel once round the
sun vary as the cubes of their mean distances fr. >m the
sun. If then T is the time for a planet moving in a
circle of radius r we get T 2 proportional to r*. l>ut
the time of a complete revolution varies inversely as
the angular velocity n, since the time multiplied by
n r (velocity)
CENTR\L ACCELEKAIION IN CIRCLE
If body moves with constant angular \<>1 >city n in cu.de of radius r, acceleration
ib n*r towards the CL-ntte.
the angular velocity must give the complete angle all
round, or four right angles, i.e. the same for all the
planets. Hence n 2 is proportional to i/r 3 so that n*r
is proportional to i/r 2 . This is of course the inverse
square law !
Newton then argued by analogy that if the gravita-
tional pull of the sun on the planets follows the inverse
square law, then the pull of the earth on the apple and
on the moon must also follow the inverse square
law. Why ? Because Newton had a profound lx lief
in the unity of the universe, in the similarity of effects
produced by similar causes that truth is independent
not only of time but also of place, so long as at difknent
times or at different places we look for the results
50 SIR ISAAC NEWTON
produced by exactly similar causes. If the motion of
the moon is to be explained by the earth's gravitation
then it can only happen on the basis of the inverse
The distance of the moon from the earth's centre is
about sixty times the radius of the earth itself. It
follows therefore that the gravitational effect of the
earth on a unit mass of the moon must be one part in
3,600 of the effect produced on a unit of mass near
the earth's surface, say, a falling apple. The accelera-
tive effect on the moon must therefore be 1/3,600 of
the accelerative effect oh the apple. The accelerative
effect on the apple is to add a speed of 32*2 feet per
second each second. Hence the accelerative effect on
the moon must be a speed of 32-2/3,600 feet per second
added each second, i.e. 0*00895 feet per second added
Is this accelerative effect equal to n 2 r, where r is
the radius of the moon's path in feet and n is the
angular velocity of the moon round the earth in true
mathematical measure, i.e. in radians * per second ?
We know r to be 6oR where R is the earth's radius
in feet. As regards n we know that the moon
describes 360 round the earth in about 27 \ days : this
makes n equal to 1/375,000, with the result that the
acceleration produced by the earth's pull on the moon
is -R/2,344 f ooo,ooo where R is the earth's radius in feet.
Everything depends upon R, the radius of the earth.
This is a very difficult quantity to measure, but Newton
lived at a time when accurate knowledge of the size of
the earth had already been obtained. Yet he was far
removed from books and he had to rely on memory.
It was commonly supposed that the size of the earth
is such that a degree of latitude is 60 English miles.
Newton adopted this view and made the complete
* A radian is the angle subtended at the centre of a circle by an
arc of the circumference of length equal to one radius.
UNIVERSAL GRAVITATION, 1666 51
circumference 360 times this, or 21,600 miles. The
radius was therefore 3,440 miles or about 18,160,000
feet. The acceleration of the moon should thus be
0-00775 feet per second added each second.
Galileo gives 0-00775, Kepler gives 0-00895. The
latter exceeds the former by nearly sixteen per cent !
" This is not equality," said Newton to himself. " My
thought has been but an idle speculation. This great
problem is not to be solved by me. Yes, I can patch
up my theory and imagine all kinds of causes to
account for the apparent deficiency in the moon's
angular motion. But I can only deal with realities,
with forces which I know something about. To
postulate mysterious agencies whose effects I cannot
measure directly is not a useful contribution to the
We must pause and observe this young man,
twenty-three years of age. By sheer genius he has hit
upon the very secret of the heavens, and carried out
calculations in which lie the germ of the complete ex-
planation of the motions of the planets. Yet Newton
does not dare to conclude that his theory is right, because
there is a discrepancy of sixteen per cent in the quan-
titative investigation. The leap of genius must not
be confounded with intellectual recklessness. The dis-
coverer must be true to himself. His ego is indeed an
invaluable ingredient of his work but it must be the
ego of honest personality, not that of selfish egotism.
We can picture the pang with which Newton abandoned
his theory, how his innate intellectual honesty struggled
with human weakness in his closet on the first floor
of the Woolsthorpe manor house the tiny room that
can still be visited and admired as the hallowed shrine
of the true spirit of discovery and conquered. If
ever the scientific method scored a victory it was in
the humble home of the widow and her orphaned
52 SIR ISAAC NEWTON
Not a word did Newton say of all this to a living
soul. He had failed and there the matter ended. It
did not really end there, for about sixteen years later
New tun discovered the source of the discrepancy and
the cause of his failure the simple fact that the value
of R he had assumed was too small, and that he should
ha\e taken it by about fifteen per cent greater !
Perhaps humanity is all the better for the apparent
failure and the delay in the ultimate success. Is not
this example of intellectual honesty and of impersonal
devotion to the cause of scientific truth as valuable
as any contribution to human spiritual values ever
made by mortal man ?
THE ANALYSIS OF LIGHT AND COLOUR, 1666
Behold, a prism within his hands
Absorbed in thought great Newton stands, . .
The chambers of the sun explored,
Where tints of thousand hues were stored.
^ ^HE Great Plague was responsible for interrupting
I an experimental investigation which turned out
^ to be Newton's main work for a decade. The
discovery of the telescope and its remarkable use at
the hands of Galileo naturally made optics in general,
and telescopes in particular, the subject of keen interest
on the part of all the scientific men of the seventeenth
century. Newton's attention was drawn to the subject
in a very natural manner. He himself records that
early in 1664, when he was still an undergraduate, he
observed and measured lunar crowns and halos.
What Newton did in optical research during the next
two years we cannot say, but we do know that in the
beginning of 1666 he bought a prism to examine the
phemonena of colours. He tells us himself that
having discovered why the telescopes of those days
were defective, he was led to consider the making of
telescopes based upon reflection. " Amidst these
thoughts I was forced from Cambridge by the Inter-
vening Plague, and it was more than two years before
I proceeded further." Newton did in fact proceed to
construct a reflecting telescope till late in 1668. It
is therefore clear that the first notions of Newton's
great discovery of the spectrum must have come to
54 SIR ISAAC NEWTON
him in 1666. We know that he was absent from
Cambridge in 1666 up to about the end of March, and
then from about the beginning of July onwards till
the end of the year ; hence it is highly probable that
Newton's first glimpses into the true nature of colour
were obtained early in 1666, and that he made some
experiments between April and June of that year.
Newton was then twenty-three and a half years of age.
A telescope is based upon the following fundamental
idea. An image of a distant object is formed by means
of a lens called the object glass and this image is
then observed by means of another lens called the
eye-piece. The construction of the most complicated
modern telescopes is based upon essentially the same
idea. It therefore seems to be an indispensable con-
dition of a good telescope to make the object glass
collect the rays from any point of the object observed
accurately to a focus. If rays from any point of the
object do not give an exact point image, then the
telescope suffers from aberration and its optical value
is diminished the picture in the telescope is indis-
tinct, which is bad for the eyesight and bad for exact
It is, however, a remarkable fact that the only form
of optical operation that brings rays emanating from
a point to an accurate and exact focus at another
point is reflection at a plane surface. The perfectly
plane mirror gives a reflection which is perfect in
sharpness of outline and of detail. Any other optical
operation, especiaDy refraction or light bending at a
plane or any other surface between one medium, say
air, and another, say glass, gives more or less blurring
This fact was soon understood and the problem of
optics narrowed down. If it is impossible to get
an exact image of all points of the object, it may
yet be possible to secure an exact image of one point
LIGHT AND COLOUR, 1666 55
of the object for scientific, especially astronomical,
purposes this would be a great thing, nearly as much
as is really needed for useful work.
Even this modest demand is not easily satisfied
in an ordinary telescope arrangement, in fact is quite
Rays OP lt OP,, OP,, etc., from the point O, are bent into the directions P^,,
PQ, PtQa, etc., when passing from air into glass ; these new directions are not
concurrent ; hence " spherical abenation."
out of the question if the surfaces of the object lens
are plane or spherical. Thus if P^Pa represent
a plane surface of separation between air and glass,
and OPj, OP 2 , OP 3 , ... are rays from a point O
striking the surface at P t , P a , P 8 . . ., then the new
56 SIR ISAAC NEWTON
rays after refraction, namely, l^Qi, P 2 Qa> PsQs -
do not pass through one point they form in fact a
very complicated bundle of rays which do not give a
sharp image point at all. The same applies to
refraction as this is called at a spherical surface
of separation between air and glass. How is this
difficulty to be overcome ?
This " spherical aberration " engaged the attention
of the mathematicians of the generation immediately
preceding Newton. When Galileo first invented and
used his telescopes he added to astronomical science an
instrument of marvellous power but the telescopes he
used were nevertheless very defective instruments,
and no doubt Galileo's blindness towards the end of his
life can be traced to the strain he imposed on his
eyesight in using these telescopes so assiduously.
The cause was taken to be the spherical aberration
just indicated, and search was made for a means of
It was the great Descartes who suggested what
appeared to btf a really good way out of the difficulty.
He looked at the problem in a somewhat different way.
Instead of assuming that lenses must have plane or
spherical surfaces he asked himself the following
question : " Given an object point O, rays from which
are to be refracted at some surface of separation
between air and glass, so as to pass through another
and image point I, what should be the form of surface
used ? " Only in one case can a spherical surface be
used, and this is of no value for telescopic purposes
it is really of fundamental importance for high-power
microscopic objectives as constructed nowadays.
Descartes found that to get the surface he wanted he
had to depart from the spherical shape, and grind the
lenses in accordance with new curves that beai his
name Cartesian ovals : he therefore suggested the
use of these new surfaces, and even devoted time and
LIGHT AND COLOUR, 1666 57
energy to the devising of machines for producing such
surfaces on glass.
Yet it was all a fallacy. In actual fact the grinding
and polishing of non-spherical surfaces on glass is on
the whole impracticable, and spherical surfaces are
the basis of applied optics to this day. But even if
perfectly ground and polished surfaces of exactly the
form indicated by Descartes' theory could have been
produced, they would have yielded practically no
improvement in the optical properties of telescopes.
It was not spherical aberration that was to blame for
the imperfection of Galileo's telescopes. The blame
belonged really to a cause of which Galileo, Kepler
and Descartes were all ignorant an ignorance all the
more striking since so many natural phenomena flow
from the same source.
The colours of the rainbow, with its promise of peace
and reconciliation after the storm, the flash of the
diamond, the colours of the prism, the charm of the
soap-bubble, why the very things observed in the
telescopes of the period, seemed to beg for elucidation
by an almost obvious principle yet the principle lay
hidden from the human understanding, and needed
the genius of Newton to give it to the world. Already
in 1666, when twenty-three years of age, Newton had
decided to experiment with the prism, and had reached
the momentous and fundamental conclusion that the
telescopes of Galileo and Kepler were incapable of
improvement, and that a new principle of telescopic
construction had to be employed?]
It seems to be impossible to say how much knowledge
of the phenomena of colour Newton had acquired when
he reached this conclusion. He did not publish an
account of his researches till five or six years later, and
in this account a clear chronology is not given. We
find moreover that when about three years later in
1669 he helped his great teacher and friend Isaac
58 SIR ISAAC NEWTON
Barrow in the publication of a set of lectures on optics,
Newton did not even then correct Barrow's quite
absurd notions about colour. We must therefore con-
clude that Newton himself was not quite clear on the
subject, even after he had abandoned attempts to
improve Galileo's telescope. The fact, however, that
Newton did reach the conclusion to discard Descartes'
idea and to turn to reflecting telescopes instead,
cannot but indicate that he had discovered the main
principle underlying such conclusion.
The fact is of course that in addition to the spherical
aberration difficulty of which the great mathematicians
before Newton were quite aware, there exists another
cause of indistinctness and imperfection in refraction
which they did not suspect, and which Newton dis-
covered. We need not devote much space to the
description of this discovery and the method adopted
by Newton to make it. Every man or woman who
claims to possess the rudiments of scientific culture
surely knows that when a beam of parallel white light
is sent through a prism so that it is deflected by
refraction, it does not emerge as a beam of parallel
white light, but rather as a bundle of beams of all
colours no longer parallel but pointing in different
directions. Newton sent a beam of sunlight of
circular section through a prism, so that it was bent
once on entry into the prism and once on emergence
from the prism : when caught upon a screen two
effects were observed. The screen gave a coloured
patch of light instead of a white patch : this in itself
was not so very unexpected, since Newton, like millions
of intelligent human beings before him, had observed
that prisms produce colours this is why prisms are
so popular for purposes of adornment round lights
and in windows. But the second effect observed was
unexpected and thought-provoking. The original
beam was circular in section : the patch of coloured
LIGHT AND COLOUR, 1666
light on the screen was lengthened in a direction at
right angles to the edge of the prism ; and it was no
moderate lengthening the patch was five times as
long as it was broad. This was completely at variance
with all contemporary doctrine on the passage of rays
Perhaps Newton did not at once solve the mystery
judiciously chosen and carefully executed experi-
White light split up into coloured rays when passing through a prism, forming
ments were yet necessary in order to explain this
new phenomenon, and these Newton carried out during
the succeeding five years. But one thing was obvious
to him. If refraction through a prism converts a thin
circular beam of light into a beam whose section is a
long strip, then clearly a telescope that depends upon
refraction through a lens cannot but produce imperfect,
coloured and blurred images. This did not depend
upon the exact shapes of the lens surfaces. Cartesian
60 SIR ISAAC NEWTON
ovals were simply irrelevant to the problem. A lens
cannot produce a clear and sharp white image of a
star colour must be introduced and cause con-
fusion : the aberration to be eliminated was not
spherical aberration but " chromatic " aberration,
error due to colour. Whatever the cause of chromatic
aberration may be, it is not produced by reflection at
any surface, plane, spherical or of any other form,
as Newton soon discovered. Hence came Newton's
decision to relinquish refracting for reflecting telescopes,
especially as three years before then, in 1663, James
Gregory of Aberdeen had already proposed this type
of instrument . But Gregory was in complete ignorance
of the cause of the imperfection of refracting telescopes,
and in any case he never made a reflecting instrument
at all. Newton discovered the cause which had
baffled the mightiest intellects of the generation before
him when he was a graduate of one year's standing,
and made a reflecting telescope with his own hands
about two years later.
The three subjects to which the youthful Newton
devoted the years immediately following his graduation,
and in which he made such remarkable discoveries so
early in his career, were an epitome of his life's work.
Fluxions, gravitation and optics these were the main
concern of the whole of his scientific life. For over
thirty years he continued to achieve conquest after
conquest. A decade he devoted largely to the prosecu-
tion of his optical researches and to the consolidation
of the great discovery of the spectrum, A second decade
he devoted to the working out and publication of his
still greater discovery of the fact and the law of
universal gravitation, the discovery that Newton is most
often remembered for and in which his influence is
still alive to-day. The subsequent decade of his
scientific life at Cambridge Newton devoted to the
further development of his astronomical work, and
LIGHT AND COLOUR, 1666 61
the consolidation of his pure mathematical researches,
notably the method of fluxions. No other man in
the history of science presents a record of devoted
service in the cause of science with such conspicuous
genius and success.
THE OPTICAL DECADE, 1668-1678
Bright effluence of bught essence increate.
Or hear'st thou rather, pure ethereal stream.
Whose fountain who shall tell ?
JOHN MILTON : " Paradise Lost," Book III
NEWTON returned to Cambridge early in 1667*
The latest recorded absence due to the Plague
was Lady Day, 1667. He said nothing to any-
body about his discoveries and ^peculations in mathe-
matics, astronomy and optics. JHis merit was obvious,
however, and on October i, 1607^ Newton was elected
Minor Fellow of Trinity College^ He could now settle
down and work without any serious economic worries,
and devote all his attention to the sciences.
There is reason to believe that as Fellow of Trinity
Newton was assigned rooms in the staircase which has
since become famous as Newton's staircase, east of
Great Court. The rooms he occupied hen were not
those pointed out nowadays as Newton's rooms, but
rather the ground floor apartments abutting on the
College Chapel. The so-called Newton's rooms, on
the right-hand side on the first floor, were occupied by
him later on.
Newton was soon busy at his researches with drills
and hammers, magnets and compasses, prisms and
materials for polishing glass and metal. He spent a
few months in Lincolnshire, staying there in December
over Christmas, 1667, and into the month of February,
1668 : but he returned to Cambridge and took the
THE OPTICAL DECADE, 1668-1678 68
degree of M.A. in March. He was elected Major
Fellow in the same year. He spent August and
September in London, no doubt for the purchase of
materials for his optical and other, especially chemical,
experiments, and then returned to Cambridge in order
to execute the design of more than two years' standing,
namely, to make a reflecting telescope.
James Gregory had proposed a reflecting instrument
consisting of two concave mirrors turned towards one
another. Light from the object to be observed was
to be reflected from one of the mirrors the wider one
to a focus in front of the smaller mirror. The latter
would reflect the light again and bring it to a focus
through a hole in the first mirror so as to be observable
by a person placing an eye-piece behind this hole.
Newton very much disliked the hole in the larger
mirror, and preferred instead of the second concave
mirror a plane mirror placed at 45 with the axis of
the telescope. The rays would thus be reflected to a
focus through a hole in the side of the telescope tube.
Newton's idea is the one usually followed nowadays,
though a variant of Gregory's form, in which the small
concave mirror is replaced by a small convex mirror
the hole in the large mirror and eye-piece behind it
being retained is represented by one very large
reflector in existence to-day. This form is known as
Cassegrain's telescope : Cassegrain was a contemporary
of Gregory and of Newton.
There is not really very much to choose between the
different forms, as Newton himself admitted. New-
ton's real merit consists in the fact that he actually
made such an instrument the first reflector in
history towards the end of 1668. It was not a great
instrument either in size or in performance. Its
aperture was one inch and its length was six inches.
Newton used a magnification of forty times, and
claimed that this was as much as could be done with
64 SIR ISAAC NEWTON
a refracting telescope six feet long. He turned the
telescope to the sky and saw with his tiny instrument
the disc of Jupiter and the then known four satellites
very nicely, and the phases of Venus with a little
While Newton was working at this instrument, and
engaging himself in researches of a chemical nature
he spent quite considerable sums of money on chemicals,
furnaces, and a " theatrum chemicum " in April,
1669 the turning point in his career was close upon
him. Isaac Barrow, a famous preacher and an
excellent mathematician, had had Newton under
observation for several years. Barrow was the first
Lucasian professor of mathematics in the university,
and had contributed with distinction to the develop-
ment of geometry and analysis. In 1669 Barrow
decided to devote himself entirely to theology and to
resign the Lucasian chair. A successor was needed,
and with remarkable vision Dr. Barrow nominated the
twenty-six year old Newton for this post. No doubt
Barrow was influenced to do this by two indications
he had received of Newton's learning and ability.
The first was Newton's help in Barrow's publication of
his lectures on optics in 1669. The second was a
paper that Newton gave to Barrow in the same year,
entitled " On Analysis by Equations with an Infinite
number of Terms," the first written statement on New-
ton's discoveries in mathematics, particularly fluxions,
that we know to have found its way into another man's
hands. Newton suggested that the paper might be
sent to John Collins, a contemporary mathematician
who corresponded with many mathematical workers
and acted as a sort of liaison between them. Barrow
received the paper in June, 1669, he sent it to Collins
on July 3ist, and three weeks later Barrow wrote
again to Collins expressing pleasure at the favourable
opinion that he had formed of the paper and divulging
THE OPTICAL DECADE, 1668-1678 65
that the author was Isaac Newton. Collins took a
copy of this paper and returned the original. It is
remarkable that Barrow and Collins, more experienced
men than Newton, also failed to realize the importance
of publishing the paper, both for Newton's own reputa-
tion as well as for the advancement of learning. It was
not till forty-two years later that the contents of this
manuscript were given to the world. In this way was
Newton's priority as the discoverer of the fluxionary
method allowed to come under a shadow of doubt,!
and the seeds of future unpleasantness sown.
(jNewton's brilliance was recognized in Cambridge, and
he was appointed Lucasian professor on October 29,
1669^ As professor Newton had to lecture once a week
one 'term each year on some mathematical topic, and
to devote two hours per week to audiences with
students who wished to consult the professor about
their work and any difficulties they might have
encountered. Newton chose to lecture on optics, for
he was then in the midst of his further researches on
the spectrum, the results of which he laid before his
students. The lectures as such were not published
till very long afterwards, when Newton had already
left Cambridge and relinquished the professorship.
Fortunately, however, his optical work was to come
before a wider audience of scientific men in a somewhat
peculiar manner. Later he lectured on algebra and
Newton did not himself have a very high opinion
of his little reflecting telescope. He made a second
instrument, of about the same size as the first, but
slightly better. The Royal Society, which had been
founded at the instance of King Charles II in 1667,
got to hear of the actual existence of a reflecting
telescope, and sent a request to Newton that he might
send them the instrument for inspection. It seems
that Newton was a little vainer about his practical
66 SIR ISAAC NEWTON
workmanship than his theoretical researches, for he
readily acceded to this request. The instrument was
sent to London, and not only the Royal Society, but
also the King, saw it and expressed admiration for it.
This telescope still exists as one of the most treasured
relics in the possession of the Royal Society to-day.
The reputation of the telescope maker began to
spread. [lie was at once proposed for election to the
Royal Society, and elected without delay on January
II, 1672!) This compliment pleased Newton very
much, and he promptly offered to communicate to
the Royal Society what he considered to be far more
important and valuable, namely, his discovery of the
spectrum and of the nature of colour. Newton's own
opinion of his discovery is interesting in view of his
general modesty and soberness of expression : he refers
to it as " being in my judgment the oddest if not
the most considerable detection which hath hitherto
been made into the operations of nature " I
[On February 6, 1672, Newton sent his paper to
Oldenburg, the Secretary of the Royal Society, and it
was published soon afterwards. By then Newton
had reached more definite conclusions about the
mysterious five-fold extension of the^ section of a beam
of light on passing through a prismT] At first Newton
looked for various and quite impossible ways of
explaining this result. But the conviction soon dawned
upon him that there must be in the divergent coloured
beam a number of beams of different colours, which
had suffered different deviations by refraction through
the prism. He found that the coloured patch could be
made white again and the section restored to its
original circular shape by taking the divergent coloured
beam through another exactly equal prism, but with
the bending taking place in an opposite sense to the
refraction through the first prism. He then examined
the light falling on various portions of the extended
THE OPTICAL DECADE, 1668-1678 67
patch on the screen. He was able to prove quite
clearly and conclusively that these lights were all
different from one another, and did actually suffer
different refractions in going through the prism.
Red, orange, yellow, green, blue, indigo, violet were
the colours thus distinguished, the bending suffered
through the prism being least for the red light, and
increasing till the greatest bending was suffered by
the violet light.
This was indeed a " considerable detection . . , into
the operations of nature." White light is not homo-
geneous : it consists of differently coloured rays of
varying refrangibility, or liability to be bent in passing
from one medium into another. A convex lens will
therefore not produce one white image, but a number of
coloured images, a violet one nearest the lens, a red
one furthest from the lens, and the other colours
ranging in between. The cause of the imperfection of
telescopes became quite obvious.
All this Newton set out in his paper to the Royal
Society. He justified in this way his making the
reflecting telescopes, and suggested that reflecting
microscopes might also be made. Let it be said at
once that the reflecting telescope of Newton was but
the forerunner of mighty instruments based upon his
construction. The hundred-inch reflector at Mount
Wilson Observatory in California is a direct descen-
dent of Newton's tiny telescope, through a long and
noble lineage of reflecting telescopes made by William
Herschel. Nothing considerable ever came, however,
of the suggested reflecting microscope.
But Newton went further. Colour became to
Newton a definite property of a ray of light, immu-
tably associated with the amount of refraction that it
undergoes in passing from medium to medium. He
attributed the colour of a body to the light by which
the body is seen and not to the body itself, and was
68 SIR ISAAC NEWTON
thus the first man to give a reasonably accurate
account of this important matter.
We have already seen that new ideas are not easily
assimilated at any time, and this was particularly the
case in the seventeenth century. Even men of science
who were themselves original workers of great merit,
failed to recognize in Newton's paper one of the
finest contributions ever made to the theory of optics.
Men of insignificant scientific stature raised objections
to Newton's experimental results, and he answered
carefully and with a good humour. This became
irksome, and Newton began to lose patience. But
Oldenburg induced him to go on, and to spend much
time and energy in correcting his adversaries, and
detecting their errors. Considerable discussion arose
over the question of the five-time extension of the
section of the beam. It was claimed by Lucas of
Liege that he had carried out the same experiment
as Newton and had obtained an extension of only
three and a half times. Both Newton and his adver-
sary maintained the accuracy of their measurements.
There can be little doubt that both were right. The
amount of " dispersion " depends upon the nature of
the prism the kind of glass used. Some glasses give
a much larger dispersion than others, for the same
amount of general bending of the beam. This was not
suspected by Newton. Had Lucas been fortunate
enough to induce Newton to go into the question of
the kinds of glass used by the two experimenters then
a discovery of capital importance would have resulted.
Newton's conviction that dispersion is always pro-
portional to general deviation led him to conclude
that it was quite impossible to eliminate chromatic
aberration in a refracting instrument. This is now
known to be untrue. By combining a convex lens of
crown glass with a concave lens of flint glass we can
make an achromatic combination, i.e. a combined lens
THE OPTICAL DECADE, 1668-1678 69
which gives an image almost (but not quite) devoid of
colour aberration. If the mighty reflectors of to-day
are monuments of Newton's genius in optical discovery,
the mighty refractors of to-day are equally imposing
monuments of the imperfection of Newton's know-
ledge and the harm that accrues to science when the
authority of a fallible human being is allowed to silence
criticism and to discourage further research. It was
only several generations after Newton's insistence upon
the amount of dispersion being so-and-so, without
paying any attention to the material of the prism,
that his mistake was discovered and rectified. Since
then refracting telescopes have become the really
accurate instruments of astronomy, the mainstay of
In his account of the spectrum and the nature of
colour Newton did not make any assumption as to
the nature of light itself. He was content to speak of
it as " something or other propagated every way in
straight lines from luminous bodies." The experi-
mental facts that he had discovered seemed to him to
transcend any theory that one might invent concern-
ing the ultimate nature of light propagation. When
Robert Hooke, an Englishman of great ability whom
we have already mentioned, and Christian Huygens in
Holland, one of the most famous scientists of that
century, raised objections to the spectrum on the
ground of the wave-theory of light which they believed
in, Newton felt that they were introducing irrelevances,
and from men of their scientific power this was annoy-
ing. He was always somewhat unwilling to face
publicity and criticism, and had on more than one
occasion declined to have his name associated with
published accounts of some of his work. He did not
value public esteem as desirable in itself, and feared that
publicity would lead to his being harassed by personal
relationships whereas he wished to be free of such
70 SIR ISAAC NEWTON
entanglements. The effects of his publishing his
optical results therefore decided Newton to desist from
such publication in the future. " I see I have made
myself a slave to philosophy. ... I will resolutely
bid adieu to it eternally, excepting what I do for my
private satisfaction, or leave to come out after me ;
for I see a man must either resolve to put out nothing
new, or to become a slave to defend it." Fortunately,
Newton did not persist in this determination except
for the fluxionary method and other pure mathematical
work, which seem to have been doomed to remain the
private possession of Newton and a few of his friends
for a long time to come.
We know very little of Newton's personal life
throughout this period. We have, however, informa-
tion on the authority of a close friend who shared rooms
with him at Trinity, that Newton developed very early
in life that forgetfulness about food and a carelessness
about his own health which became characteristic of
him in later life. He would often work till very late
and miss restful sleep because of his work. At the
age of thirty he was already turning grey. He
suspected himself to be inclined to consumption and
made medicines for his own use. Newton was indeed
fond of dosing and curing himself. " His breakfast
was orange peel boiled in water, which he drank as tea,
sweetened with sugar, and with bread and butter."
When Newton caught a cold he took to his bed and
cured it by perspiration. All this reads like the life
of a bachelor, far from the help of mother or wife,
doing things for himself in a clumsy way and living for
the work on which he is engaged.
Newton was a kind man, sincerely pious and an
influence for good in many ways. As regards his
financial position, though he obtained various sums
of money from his mother before being elected to
the Lucasian chair, we may surmise that the scanty
THE OPTICAL DECADE, 1668-1678 71
yield of the farms at Woolsthorpe and Sewstern was
not overmuch for the needs of Mrs. Smith and the
three children by her second marriage. Newton was
thus left to his own resources, which were not very
great as his chair was only moderately endowed.
He was also very free with his money, bestowing
loans and gifts upon relations and friends with con-
siderable liberality, and spending freely upon his
It therefore became a matter of considerable concern
to Newton that his College Fellowship was soon to
expire, so that he would have to live upon the stipend
of the Lucasian chair alone. In order to continue to
hold his fellowship Newton would have had to go into
holy orders. He declined to do this, and instead made
an application to the King for a dispensation allowing
him to retain the fellowship as a layman and as Lucasian
professor. The petition was granted in April, 1675, an
act of royal grace which does much to whiten the
character of the merry monarch.
Why did Newton refuse to go into orders ? He was
a man of excellent character, sincerely and profoundly
moral in his opinions and in his practices. He believed
in the fundamentals of religion and even, as we shall
see, wrote much on theological matters. It is clear that
Newton desired as complete freedom in theological
thought as in scientific belief, and refused to be bound
in any manner. He did not accept without questioning
all that was taught by the prevalent churches. His
faith was that of a profound and independent thinker
and investigator, seeking for the causes of all effects
and for the unifying cause underlying all things, rather
than that of an implicit believer in doctrines laid down
by ecclesiastical authority.
These economic disturbances of Newton's equanimity
are mirrored in a remarkable manner by his relation-
ship to the Royal Society. A fellow of this body had
72 SIR ISAAC NEWTON
to pay an entrance fee of two pounds, and a continuous
subscription of one shilling per week. In March, 1673,
Newton wrote to the secretary Oldenburg resigning
his membership. He gave as his motive the fact that
he lived too far from London to be able to take full
advantage of the meetings of the society. Oldenburg
must have known better, for he offered to get Newton
excused the shilling per week payment, and Newton
himself raised no objection to an application to this
effect being made to the Council of the Royal Society.
Oldenburg did not present the application at once;
possibly he waited to get a few more such applications
to be dealt with at the same time. In January, 1765,
he mentioned " that Mr. Newton was now in such
circumstances that he desired to be excused from the
weekly payments," and Newton and others including
Robert Hooke were granted this relief. It is a
pleasing thought that the greatest minds of the day
had to submit themselves to what must have been
felt as a humiliation in order to be relieved of the
payment of one shilling per week I
The scientist does not work for reward. The
impelling motive is not personal gain or even personal
fame : it is the insistent desire of the healthy human
mind to know how Nature manifests herself around us,
and the causes of these manifestations. Scientific men
and women are continually giving of their best in the
onward march of knowledge ; they place at the service
of the community their powers and their energies.
By membership of learned societies they even pay for
the publication of the results which they deduce, often
at their own expense and without interest or encourage-
ment from anybody. Surely a community that has
so much to spend on personal luxuries, and on fashion-
able stars in the theatre and on the screen, could devote
a little more on the fostering of scientific research and
on making the task of the worker easier by removing
THE OPTICAL DECADE, 1668-1678 78
all anxiety of economic embarrassment ? Two and a
half centuries have passed since then and some improve-
ment has taken place in this respect, but Great Britain
has much leeway to make up even now.
[_The discovery of the spectrum was one of the most
important events in the history of optics, and indeed,
in the history of science. It has led to developments
in all branches of natural knowledge) The discovery
of the black lines in the solar spectrum early in the
nineteenth century gave us spectrum analysis, which
has revolutionized physics, chemistry and astronomy.
Modern astronomy, rightly called ^Astrophysics, con-
sists essentially of the application ofThe spectrum to
heavenly phenomena. By its means we discover the
constitution of the stars, their motions towards us
and away from us, their distances when too remote to
be measured directly, the events on the sun's surface
which reveal electro-magnetic fields and disturbances
of tremendous significance. The spectrum has by the
work of Bohr and others given us an insight into the
ultimate constitution of matter, and led to the initiation
of the quantum theory, the implications of which we
can as yet hardly guess. The spectrum has helped
to establish Einstein's gravitational theory, and led to
the discovery in the heavens of matter as immensely
denser than the matter on our earth as the giant stars
are lighter than our earthly matter.
It is not possible in this book to give a detailed
account of all Newton's optical work, and a mere
catalogue of discoveries will convey little to the general
reader. Yet a few words on some of Newton's
work will illustrate the magnitude of his powers
and the influence he exerted on subsequent develop-
Newton not only applied the reflecting principle to
the microscope, a suggestion that has not been very
fruitful, but he also made the capital proposal that it
74 SIR ISAAC NEWTON
would be an advantage when using ordinary refracting
microscopes to employ light of one colour, or mono-
chromatic light. While working with the plane mirror
in his reflecting telescope Newton saw how imperfect
reflection from a metallic surface is bound to be, and
he hit upon an idea without which the powerful modern
binoculars would be impossible. This was that in
view of the high refractive index of glass, an isosceles
right-angled prism of glass could be used as a reflector,
giving much better results than metals.
Discoveries of great theoretical importance were
communicated to the Royal Society at the end of
1675 in connexion with the colours of thin films of
transparent matter. It is of course well known that
very thin plates of transparent matter give different
colours. The beauty of the soap-bubble has been
immortalized in a famous picture. What are these
colours due to ? Robert Boyle, famous for his law
connecting the volume and pressure of a gas, and
Robert Hooke, observed the phenomena in mica
plates, but could not discover the relation between
the colour produced and the thickness of the plate
because of the extreme minuteness of the latter.
Newton hit upon a beautiful and ingenious idea which
we still use in our physical laboratories in Newton's
rings and in other applications.
The tangent to a circle at any point hugs the circle,
and the deviation of the circle from it is very small
even for considerable distances along the tangent, if
the radius of the circle is large enough. If A is the
point of contact of the tangent and P is a point not
too far away on the circle, while PT is perpendicular
to the tangent AT at A, then TP = TA 2 /2a where a
is the radius, supposed large. Thus, if the radius is
50 feet and TA is one-twentieth of an inch, we get for
TP 1/480,000 of an inch. If TA is one-tenth of an
inch, TP is 1/120,000 of an inch. If TA is an inch,
THE OPTICAL DECADE, 1668-1678 75
TP is 1/1200 of an inch. If then we take a flat glass
plate and put into contact with it the spherical surface
of a lens, with radius 50 feet, we have within a distance
of one inch from the point of contact a film of air which
varies from zero at the cenree to 1/1200 of an inch at
the edge. Not only is the film thin enough to produce
* 5 *
s I s
MONOCHROMATIC INCIDENT LIGHT
Alternate bright and dark rings by transmitted light ; alternate dark and bright
ngs by reflected light ; produced by thin air layer between a flat and a curved
colours like those of the soap-bubble, but we can also
calculate the thickness of the film at any measured
distance from the point of contact.
When Newton observed white light transmitted
through the film or reflected from the film he saw
coloured concentric rings, in which the colours were
by no means so simply arranged as in the spectrum.
76 SIR ISAAC NEWTON
On using light of one colour, however, the appearance
became very much simplified, less beautiful of course,
yet easier to understand. Newton found that by
reflected light of any particular colour he got a circular
dark patch in the centre, then a ring of that colour,
then a dark ring, then another ring of that colour,
then a dark ring again, and so on up to about twenty
rings. With red light the successive radii were larger,
with violet light they were smaller. Newton also
found that the transmitted light gave a circular light
patch in the middle, then a dark ring, then a light ring,
then a dark ring, and so on, the radii being exactly
the same for transmission and reflection in the case of
any given coloured light, but lightness and darkness
interchanging from one to the other. The radii were
found to be proportional to the square roots of the
successive numbers i, 2, 3, 4, etc., so that the air
thicknesses at the successive circumferences were
proportional to the numbers i, 2, 3, 4, etc. them-
Newton at once concluded that a ray of light cannot
have exactly the same properties at all points along
its length. There must be variations in these proper-
ties, " fits " as Newton called them. It is clear that
a ray of light of any given colour prefers to be trans-
mitted for a certain very short distance depending
on the colour itself, then prefers to be reflected for an
equal distance, then prefers to be transmitted for such
a distance, and so on indefinitely. A ray of light thus
has a space-period depending upon its colour, shortest
for violet, getting longer for indigo, blue, green, yellow,
orange, and being longest for red.
One can think of many objections to this theory of
fits ; but the most disconcerting feature about this
matter is the way in which this experimenter of genius
failed to grasp the (now) obvious implication of his
beautiful experiment. Surely there must be a periodi-
THE OPTICAL DECADE, 1668-1678 77
city along a ray of light propagation, and this must
be in the form of a wave, colour being in fact a property
associated with the space-period or wave length ?
Why did not Newton postulate a wave-theory and use
the great principle of interference ? No great origin-
ality was required, since both Hooke and Huygens
had used the wave-theory in their controversies with
Newton, and Hooke had even announced the principle
Strange as it may appear to us now, Newton refused
to accept a wave-theory of light. Did the opposition
of Hooke and Huygens to Newton's discovery of the
spectrum, based upon their wave-theory, prejudice
Newton against such a view ? It is hardly credible,
for Newton was too honest a thinker to be affected in
this way. The fact is that Newton was severely
practical in his conceptions. He always desired to see
or feel, so to say, any natural force or other agency
before he would accept it as an explanation of observed
phenomena. His was the kind of mind that would
interest itself in proving by direct observation the
daily rotation of the earth and its annual revolution,
that would have welcomed with tremendous joy
Bradley's discovery of aberration as proving the latter
and Foucault's pendulum as proving the former.
Of course Newton was curious to explain why these
fits existed and he did in fact invoke an " ether " to
explain this and other phenomena. He supposed
that a fluid ether permeates all space, whether occupied
by matter or not, but that the density of the fluid
varies from point to point. In this way Newton
explained many properties of matter. As regards
light he took it to be due to the very fast propagation
of very tiny corpuscles, which are acted upon by the
particles of the ether and so receive this property of
alternate fits of preference for transmission and for
reflection. This view he expressed in 1675 and he
78 SIR ISAAC NEWTON
developed it a few years later in a letter to Robert
Boyle. Apparently, however, an ether the existence
of which he could not prove directly, was not
palatable to Newton, and he rejected the ether
to be revived later in query form when universal
gravitation was added to the things requiring ex-
By means of his theory of fits Newton was able to
make considerable advance in the explaining of trans-
parency and opacity, and of the colours of different
bodies. Transparency and opacity depended, accord-
ing to Newton, upon the sizes of the spaces between
the ultimate particles of a body, while the colour of
the body depended upon the sizes of the ultimate
particles themselves. It would take us too far to
discuss these views in detail. One thing we can say,
however : they represented the first rational set of
opinions ever put forward on the subject, and
were a tremendous advance on the views held
at that time by the greatest of physicists and mathe-
Another important optical experiment carried out
by Newton referred to what we" nowadays call diffrac-
tion. Light is supposed to travel in straight lines so
long as no refraction takes place. Hence, in uniform
and still air no deviation from rectilinear propagation
should occur. This is not the case. Light rays do
bend round a corner just as sound bends round a
corner. In the case of light, however, the bending
can be detected only by means of very careful observa-
tion. An Italian, Grimaldi, first obtained the bending
and the result was published in 1665. In 1674 Hooke
carried out further experiments and betrayed his genius
by suggesting the principle of interference in order to
explain the phenomenon. Newton carried out diffrac-
tion experiments at about the same time. He cast
the shadow of a human hair upon a screen and found
THE OPTICAL DECADE, 1668-1678 79
the shadow to be much wider than the thickness of
the hair, and to exhibit coloured fringes. He did not
accept Hooke's explanation which is the right one
and attributed the phenomenon to the possibility of
flexibility in a ray of light. Rays of different colours
have different flexibilities. As a ray passes the edge
of a body a wave-like effect is produced on the ray,
giving it a shape like that of an eel ! Rectilinear
propagation is upset, and colours are introduced. This
queer explanation was published nearly thirty years
later in Newton's " Optics."
Why Newton should have been reluctant to accept
the wave-theory of light, while prepared to postulate
these eel-like motions, it is difficult to explain. Personal
idiosyncrasy is as much the prerogative of genius as
of lesser minds. Newton filled the universe with an
ether in order to account for the fits in a remote and
indirect manner. Yet he declined to follow Huygens
and Hooke in the wave-theory and in interference.
The consequences to science were very unfortunate.
When Newton had become famous as the discoverer
of the law of universal gravitation and had explained
the motions of the planets in a manner unique in
scientific history, the prestige of Hooke and of the
great Huygens could not prevail against his renown.
The wave-theory of light fell into disrepute. It was
not till more than a century later that the theory was
rehabilitated by the work of the Englishman Young
and the Frenchman Fresnel. The hero-worship
accorded to genius has its vicious as well as its virtuous
side. For genius is but human after all : it is liable
to honest mistake and even to prejudice and to passion.
Science should stand above all human considerations.
It must not bend the knee to any human authority.
It must rest on honest research, based upon complete
intellectual independence. The raw schoolboy may be
right where the sage of mighty repute is mistaken.
80 SIR ISAAC NEWTON
The weight of Newton's authority delayed optical
progress for many generations. It was not Newton's
fault, of course ; it was the fault of the lesser men
who followed him and mistook idolatry for sincere
THE GRAVITATIONAL DECADE, 1678-1687
If with giddier girls I play
Croquet through the summer day
On the turf,
Then at night ('tis no great boon)
Let me study how the moon
Sways the surf.
MoRriMER COLLINS : ' Chloe, M.A.."
WE now enter upon the second or gravitational
decade of Newton's scientific career. The
period between 1668 and 1678 was not exclus-
ively devoted to optics. His famous paper on the
method of infinite series and fluxions was written in
1669. He wrote a second treatise on fluxions in 1672,
but this also remained unpublished. He communi-
cated with Huygens concerning gravitation in January,
1673, and he wrote a paper for the Royal Society on
the excitation of electricity in glass in 1675. In the
same year Newton wrote to Nicolas Mercator, immor-
talized in the map projection called after his name,
concerning the librations of the moon, the fact, namely,
that although on the whole the moon always turns the
same half of its surface to the earth, we do notice
slight changes in this respect, as if the moon were
oscillating from one side to the other. Newton
explained this satisfactorily as being due to the uniform
rotation of the moon about its axis in exactly the time
it takes to complete a revolution round the earth
this motion of revolution is not uniform, so that some-
times the moon has apparently rotated too much, at
82 SIR ISAAC NEWTON
other times too little, in relation to the angle through
which it has revolved round the earth.
In the midst of his scientific preoccupations Newton
even found time to discuss agricultural matters. He
was perhaps making inquiries on behalf of his college,
but in September, 1676, he wrote to Oldenburg on the
question of planting apple trees for the manufacture
of cider 1 He wished to know : " What sort of fruit
are best to be used, and in what proportion they are
to be mixed, and what degree of ripeness they ought
to have ? Whether it be material to press them as
soon as gathered, or to pare them ? Whether there
be any circumstances to be observed in pressing them ?
or what is the best way to do it ? "
In the same year Newton wrote to the great German
philosopher and mathematician, Leibnitz, concerning
his method of fluxions. Leibnitz sent a reply in which
he gave an account of the differential calculus with the
notation in vogue to-day, and which Newton must at
once have seen to be the same thing as his own fluxions,
differing from his invention only in the notation.
But Newton's attention was soon directed to astro-
nomy and gravitation. We may assume that the
abortive calculations made at Woolsthorpe in 1666
never quite dropped out of his memory. The problem
of planetary motions was too insistent and the failure
too tantalizing to leave a man like Newton quite
unaffected. Meanwhile another man had been writing
on the subject, Robert Hooke.
Hooke was a man of great genius, but owing to his
preoccupation with all sorts of matters he never quite
finished off any great line of research, and consequently
never reaped the full fruits of the seeds that he sowed.
Newton was on the other hand a remarkably successful
investigator of singular stability of character and
steadiness of application. We have already seen that
Hooke and Newton had had occasion to dispute over
THE GRAVITATIONAL DECADE, 1678-1687 88
optical matters. Hooke had also treated the younger
Newton somewhat unkindly on the occasion of his
first communication to the Royal Society, when
Newton's reflecting telescope was under inspection.
Hooke may have seen in Newton the younger and
greater rival who did the things that Hooke might
have done if not anticipated by Newton. A mild
jealousy of Newton grew up in Hooke's mind, and
perhaps a slight suspicion of Hooke entered Newton's
Similar unfortunate circumstances arose soon in
connexion with gravitation. While Newton was specu-
lating on his failure at Woolsthorpe, Hooke sent to the
Royal Society, in 1666, a paper on the question of
how the earth's gravity varies with height above the
earth, making the important suggestion that the force
of gravity could be measured by means of a " swing
clock ' ' or pendulum. He followed this up with another
paper in the same year, suggesting that the planetary
motions could be explained by means of an attraction
towards the central body. This vague idea, which
had occurred to several others before then, took more
definite shape in a third publication which appeared
in 1674. In this work Hooke quite definitely postu-
lated universal gravitation, stating that each heavenly
body not only keeps itself together by its own attrac-
tion, but also exerts a force upon every other heavenly
body. He did not yet know what law to use, how the
gravitational force exerted by a body depended upon
the distance from this body ; but in 1679 Hooke wrote
to Newton and made the assertion that if the earth's
gravitation varied inversely as the square of the
distance the curve described by a projectile would be
an ellipse, with a focus at the centre of the earth.
In spite of all this, however, Hooke's claim to
consideration in the question of priority in this
matter could have been of little weight. Newton had
84 SIR ISAAC NEWTON
discovered the inverse square law thirteen years before
by direct deduction from Kepler's third law of planetary
motions. He had been held up by a quantitative
discrepancy which turned out to be due to a quite
irrelevant circumstance, namely, his ignorance of the
correct size of the earth. Hooke's suggestion that the
inverse square law would yield elliptic motion round
a focus was not accompanied by a proof. It was
Newton who established independently, and by
brilliant mathematical reasoning, that all the facts of
planetary motion then known could be accounted for
by universal gravitation according to the inverse square
law. By universal consent Newton was acclaimed as
the discoverer of the secret of heavenly mechanics.
This reacted upon Hooke's mind with some unpleasant
If Newton had been acquainted with correct values
of the earth's radius published thirty years before
his Woolsthorpe calculations, would he have made
his great gravitational achievements much earlier ?
Possibly in his Lincolnshire exile Newton had no means
of referring to books on the subject, but when he did
get back to Cambridge he should have become
acquainted with the correct radius of the earth.
Accurate measurements by the Frenchman Picard
were communicated to the Royal Society on January
n, 1672, the very meeting at which Newton was
elected a fellow and at which his reflecting telescope
was exhibited, and published in the Transactions in
1675 : Newton cannot have missed seeing these results.
It is a remarkable fact nevertheless that he did not
take up the matter again until his attention was
directed to it by Hooke himself.
Robert Hooke became Secretary of the Royal Society
in 1678, after Oldenburg's death. He wrote to Newton
asking him if he had something new to communicate
to the society. Newton replied with a dissertation on
THE GRAVITATIONAL DECADE, 1678-1687 85
the diurnal rotation of the earth. The reason why the
earth's rotation remained undiscovered till so recently,
and why some cranks still doubt it to-day, is simply
/ / ^
PALLING BODY AND ROTATING EARTH
Path of stone dropped from A lies in that plane through the centre of the earth
which touches B's circle of latitude at the point B. The stone falls east of B' (the
new position of B when the stone reaches the ground) and south of it.
that this rotation takes place in a perfectly smooth
manner, with all the things on the earth accompanying
it in its rotation. No differential motions are visible
86 SIR ISAAC NEWTON
to us : the solid earth rotates, the waters of the ocean,
the air, houses, trees, we ourselves all goes with the
earth. How can the supposed rotation be distinguished
from a state of rest of the earth ?
It was Newton who saw that this very fact that all
things on and near the earth accompany it in the
diurnal rotation could be used to demonstrate the
rotation ocularly. For consider a point A vertically
above any point B of the earth's surface, so that AB
is along the extension of a radius from the earth's
centre. In the diurnal rotation the line AB is carried
with it bodily ; hence the point A has a velocity, due to
this rotation, greater than that of B, since it is further
than B from the common axis of rotation. Now let
a body be dropped at A. During the fall it receives
downward acceleration taking it to B. But it also
had initially a horizontal velocity west to east greater
than that of B. Hence the falling body will not reach
the earth exactly on B, but slightly to the east of B.
The deviation would be very small indeed : for AB =
100 feet, the deviation in London would be T V inch.
Newton suggested this as a possible experiment a
straightforward test of the earth's rotation.
The suggestion was adopted and Hooke was
appointed to carry it out. Before doing so, however,
he examined the matter more carefully and came to
the conclusion that Newton was not quite right. If
B is on the Equator, then Newton's argument is
faultless. But if B is not on the Equator, then the
deviation will not be exactly to the east : it will be
also a little to the south in the northern hemisphere,
to the north in the southern hemisphere. It is not
difficult to understand why this should be the case.
The body during its fall is pulled along AB. Relative
to B the initial motion of A is to the east. Hence the
body's fall takes place in the plane containing the line
AB and touching the cone described by AB, along the
THE GRAVITATIONAL DECADE, 1678-1687 87
line AB. This tangential plane lies outside the cone
and so cuts the earth in a circle which lies outside the
parallel of latitude at B : in other words, the body
must come a little south as well as east, since it is the
parallel of latitude that defines east and west.
Newton had missed this point, and at once admitted
it when his attention was drawn to it. Hooke carried
out the experiment and verified the deviation in
December, 1679, the first ocular proof in history of
the rotation of the earth ! It was the year of the
Habeas Corpus Act.
In connexion with this investigation the question
arose between Newton and Hooke as to what the path
of a body actually is under the earth's attraction,
taking this attraction to vary inversely as the square
of the distance. Newton conjectured that the path
would be a spiral curve. Hooke dissented from this
and asserted that the path would be an ellipse with a
focus at the centre of the earth. Newton himself said
about this : " And tho' his (Hooke's) correcting my
spiral occasioned my finding the theorem, by which
I afterwards examined the ellipsis : yet am I not
beholden to him for any light into the business, but
only for the diversion he gave me from my other
studies to think on these things, and for his dogmatical-
ness in writing, as if he had found the motion in the
ellipsis, which inclined me to try it, after I saw by
what method it was to be done."
It is clear that Hooke could not prove his assertion :
it was a guess, based upon his extending the idea of
Kepler's laws of planetary motion to the motion of a
projectile under the earth's gravitation. For this
Hooke deserves great credit, yet the real discoverer
was Newton, for it was Newton who turned Hooke's
useless guess into a certainty, being impelled thereto
by Hooke's " dogmaticalness in writing." Newton
was able to construct a proof of the proposition that a
88 SIR ISAAC NEWTON
body moving under an attraction towards a fixed point
varying as the inverse square of the distance from this
point, describes an ellipse with a focus at the centre of
This was a result the importance of which could
hardly be exaggerated, and Newton should have
proceeded now to complete a theory of the solar
system. But, having proved the elliptic motion,
Newton " threw the calculations by, being upon other
studies ; and so it rested for about five years." He
was making alloys for metallic mirrors one can only
wonder whether they were important enough to make
Newton " throw by " the calculations upon which his
greatest fame in human history was destined to rest.
He corresponded with the Astronomer Royal, Flam-
steed, about the great comet of 1680, and the views
Newton then expressed make it clear that he had not
yet reached a correct understanding of cometary
motions. If he had paid more attention to the train
of thought roused by Hooke, he would not have held
these erroneous views.
No apology need be offered for Newton's apparent
indifference to the matter. Evidently he was still
under the influence of his Woolsthorpe failure to
explain the moon's motion by the earth's gravity.
He could not deal with the motions of the planets
under an attraction towards the sun, without dealing
at the same time and on the same principle with the
moon's motion round the earth. To Newton's practical
mind the latter was even the more important aspect,
for only in the case of the earth's gravity could he
examine a really obvious and measurable force a force
that enters into all the phenomena of daily life. So
long as the moon did not respond to his calculations
he had no right to postulate universal gravitation as
the cause of the planetary and lunar motions.
For some reason or another Newton's attention had
THE GRAVITATIONAL DECADE, 1678-1687 89
not been drawn to the more correct value of the earth's
radius. He had taken it to be given by sixty English
miles for a degree of latitude. The correct value is
much more. Picard's value was 69-1 miles, a difference
of over fifteen per cent. It would not have escaped
the notice of a mind like Newton's that this was just
the quantity required to correct his calculations of
1666. Yet it was not till June, 1682, that Newton
became fully aware of Picard's measurements or was
it that only then did it strike him how these measure-
ments would affect his calculations ? We are told
that at a meeting of the Royal Society in June, 1682.
conversation turned upon Picard's work. Newton
noted the result and on his return to Cambridge took
up the Woolsthorpe calculations once again. Becoming
conscious of the approaching almost perfect agreement
between his theory and fact, Newton, the story relates,
became so agitated that he was forced to entrust the
arithmetic to a friend. Eventually the truth emerged.
The force which drags the apple to the earth is the
force that directs the moon round the earth. The
daring suggestion that the heavenly bodies move under
the same kind of forces and obey the same laws of
motion as the earthy matter around us was vindicated.
The road became quite clear for what may be described
as the grandest generalization ever made in human
Apparently Newton hardly ever published a dis-
covery without being urged to do so by others. Even
when he had arrived at the solution of the greatest
problem that astronomy has ever had to face he said
nothing about it to anybody. Fortunately other men
were interested in the same problem. These were the
three Englishmen, Robert Hooke, Sir Christopher
Wren, excellent mathematician and brilliant architect,
and Edmund Halley. Edmund Halley was twelve
years younger than Newton, and a man of great
90 SIR ISAAC NEWTON
ability, who, in 1684, had already done a number of
important pieces of scientific and astronomical work,
especially on comets. He became interested in the
problem of gravitation and in January, 1684, he
deduced from Kepler's third law that the sun's gravi-
tation must vary inversely as the square of the distance
in other words, he did in 1684 what Newton had
done in 1666. He tried to deal with the much more
difficult problem of finding the path of a body moving
under such an attraction, but he failed. He therefore
sought out Wren and Hooke and asked them if they
could supply what he could not achieve. Apparently
both of them had deduced the inverse square law from
Kepler's third law. But as regards the question of
finding the path under such an attraction, Wren
admitted he could do nothing with this bigger problem,
while Hooke made the statement that upon the inverse
square law " all the laws of the celestial motions were
to be demonstrated, and that he himself had done it."
Wren thereupon made a sporting offer that if Hooke
or Halley could produce the mathematical proof,
instead of the mere assertion, within two months, he
would present the discoverer with a book of forty
shillings. Hooke again said " he had it, but that he
would conceal it for some time, that others trying and
failing might know how to value it when he should
make it public." But he never produced any such
proof, and Halley, tired of waiting for it, decided to
apply to Newton.
The momentous interview took place in August,
1684, about half a year before the death of King
Charles II. Halley visited Newton at Cambridge, and
came straight to the object of his visit. " What would
be the path of a planet under a gravitational attraction
varying inversely as the square of the distance ? " he
asked. " An ellipse," came Newton's reply without
hesitation. " How do you know ? " asked Halley.
THE GRAVITATIONAL DECADE, 1678-1687 91
" I have calculated it," answered Newton. Halley
naturally wanted to see the proof, but Newton had
apparently not paid much attention to the matter for
some time and so could not immediately find his notes
on the subject. He promised to let Halley have the
Was Halley confident that Newton's proof would
really be forthcoming ? After all, his success with
Newton was not very dissimilar from his success with
Hooke, who had also claimed to have a proof and had
not yet produced it. The fact that Halley took the
trouble to go to Cambridge to see Newton shows,
however, that already he had learned to admire
Newton's genius and that he had complete confidence
in Newton's ability to establish any claim he might
make. In this he was not disappointed. Newton could
not find his original notes, but he constructed the proof
again after a little trouble and sent it to Halley
within three months of the latter's visit to him.
Halley 's joy was unaffected. He was a man who
could see gladly the success of another greater than
himself. He decided that such a discovery could not
remain unpublished. He visited Newton again and
found that the latter had meanwhile prepared a brief
account of the motion of a body under a force directed
to a fixed centre, particularly when the force varies
inversely as the square of the distance, in which case
the path is a conic with a focus at the centre of force.
Newton had already lectured on the subject as Lucasian
professor. Halley made Newton promise to send this
short treatise " De Motu " to the Royal Society, a
promise that was communicated to and welcomed by
the society on December 10, 1684.
Great events were taking place in England then.
Surrounded by intriguing parties who demanded
opposite kings, the King was in perplexity both as to
his foreign relationships and as to the question of
92 SIR ISAAC NEWTON
summoning Parliament to learn the will of his people.
In the midst of it all, on February 6, 1685, the King
died of apoplexy. He was buried in Westminster
Abbey eight days later, and a perplexed people saw
with mixed feelings the accession of Charles' brother,
King James II. It has been said that the reign thus
ended was the worst reign in English history : yet let
us remember that Charles had founded both the Royal
Society and the Royal Observatory, Greenwich, and
that he had had the grace to do an act of decency to
Newton in allowing him to retain his Trinity fellowship
without going into orders.
It was in the midst of this national commotion that
Newton wrote out his paper on planetary motions, and
it was received by the Royal Society while the dead
King was awaiting burial. Newton himself indicated
that he was preparing a larger treatise on the subject,
and in April, 1685, he began the preparation of his
Newton was forty-two years of age and at the very
height of his mental powers. If he showed greatness
as a physical experimenter in his optical work, he was
soon to prove himself even greater as a physical and
mathematical thinker. Let us state clearly what was
involved in the task he had undertaken. In the first
place, the principles of dynamics had to be thoroughly
grasped and clearly formulated, namely, that the
absence of force or the balancing of the forces acting
on a body means uniform speed in constant direction,
without any acceleration, while any change in speed
or in direction of motion of a body must be accounted
for by a force or resultant of forces, proportional to
the acceleration and acting in the same direction.
Secondly, the type of force appropriate to the problem
of planetary motion had to be considered and the
inverse square law deduced. Thirdly, the physical
reality of this attraction had to be proved, as presented
THE GRAVITATIONAL DECADE, 1678-1687 93
by the motion of the moon round the earth, the
gravitational effects of which we experience daily and
can measure accurately. Fourthly, the law of gravi-
tation had to be applied in its general form to the
planets and the motions as given by Kepler's laws
accounted for accurately. For this purpose new and
more powerful mathematical methods were required,
and Newton had to invent them. Finally, the whole
solar system had to be considered under the aspect of
universal gravitation, and motions of satellites and
comets explained, precession and tides brought within
the ambit of scientific research.
A mighty task this was which could be accomplished
only by a man specially favoured by the gods. Popular
imagination has been captured by the third point, the
association of the moon's motion with the fall of the
apple and rightly so, for this physical extension from
the earthly to the celestial is one of the most significant
steps in the revolution of ideas that Newton's work
has brought about. But what exhibited Newton's
powers to the full were the fourth and fifth points on
which he laboured during the next two years.
Newton was not content with the astronomical
observations of the older astronomers, and fortunately
he found at hand a man prepared to give him the
latest and best results. This was John Flamsteed,
whom we have already mentioned as having corre-
sponded with Newton a few years before about comets.
He was a remarkable observer of the heavens and was
appointed Astronomer to King Charles II at the early
age of twenty-nine, in 1675. The Greenwich Observa-
tory was buijt and Flamsteed headed the line of
eminent astronomers that have adorned the post of
Astronomer Royal. It was Flamsteed who gave
Newton the best information possible about the orbit
of Saturn, about the motions of the satellites of
Jupiter and Saturn the only satellites then known
94 SIR ISAAC NEWTON
besides the moon about the tides, about the flattened
appearance of Jupiter's disc. For many years New-
ton depended upon Flamsteed for the facts upon
which he built up the law of universal gravitation, and
verified the consequences that flowed from the law.
The first part of the work was soon ready ; it was
the treatise " De Motu " more fully developed, forming
Book I of the complete work. The second part or
Book II was ready by the middle of the year 1685.
Both books dealt with the theoretical aspects of
dynamics, especially as required for application to
astronomy. The third part, or Book III, was a much
more difficult task, as in it Newton had to give detailed
applications of his theory to the observed planetary
motions and other phenomena in the heavens. Finally,
on (April 21, 1686, Halley announced to the Royal
Society that " Mr. Isaac Newton has an incompar-
able Treatise of Motion almost ready for the press."
On April 28th a manuscript entitled " Philosophise
Naturalis Principia Mathematica " (The Mathematical
Principles of Natural Philosophy) was presented to the
society^JAs a matter of fact, this manuscript only
contained Book I, but the importance of the whole
work was speedily recognized and Halley was asked
to report to the Council on the question of having the
book printed. As the Council dallied in the question,
the society resolved, at its meeting of May igth,
" That Mr. Newton's work should be printed forthwith
in quarto." Still nothing was done, and on June 2nd
the society adopted a most remarkable resolution :
" That Mr. Halley undertake the business of looking
after it, and printing it at his own charge, which he
engaged to do " !
This is an interesting sidelight on the way scien-
tific men who are enthusiastic about their subjects
are prepared to face personal inconvenience and
loss in the furthering of their aims. Halley was not a
THE GRAVITATIONAL DECADE, 1678-1687 95
particularly rich man and he had a wife and family.
But when he realized the state of the Royal Society's
finances he guessed that Newton's book would never
be printed if it had to depend upon the society defraying
the cost. Apparently the Royal Society had depleted
its exchequer by printing a work on fishes, and in spite
of the members' admiration for Newton's work they
could not muster enough enthusiasm to give this
admiration a practical form. Halley therefore decided
that cost him what it may the book must be printed,
and just as Halley had discovered Newton's genius in
the matter of his gravitation theory, so it was Halley
who took the risk of shouldering the financial burden
involved in giving it to the world.
Halley was a distinguished man of science in his
own right, and was to occupy the highest astronomical
post in England, that of Astronomer Royal, and to
give to the world the first prediction of the return
of a comet. Yet, if Halley had done nothing more
than secure the publication of the " Principia " he
would have been assured of the everlasting gratitude of
If Halley in this way shielded Newton from financial
worries, he could not shield him from other unpleasant-
ness. Amidst the eulogies that greeted the presenta-
tion of Newton's manuscript, a discordant note had
been struck by Hooke. We can easily imagine the
feelings of Hooke at seeing the prize for which he so
ardently yearned snatched from his grasp. While he
had been speculating, Newton had worked and reached
a happy conclusion of his labours. Hooke could not
deny the great value of Newton's mathematical proof
that the inverse square law of universal gravitation
explains all the planetary motions then known, but
he claimed that the idea to use the inverse square law
had been given to Newton by himself.
This was really a foolish claim to make, since the
96 SIR ISAAC NEWTON
fundamental idea had occurred to several people before
Hooke, and even in Hooke's time there were Halley
and Wren who had deduced the inverse square law
from Kepler's third law independently of himself and
of one another. It was therefore very likely that
Newton, whose genius was known to excel that of any
one of this trio, had discovered this for himself, before
Hooke had suggested the inverse square law to Newton
in 1679. As we know, Newton made this discovery as
early as 1666, and when told of Hooke's claim, Newton
lost his equanimity and usual sense of fairness to such
an extent as to retort that, so far from Hooke having
suggested the inverse square law to Newton, Hooke
had got the first idea of this law from others, and even
from a letter that Newton had written to Huygens on
the subject in 1673, through the secretary of the
Royal Society, Oldenburg, and a copy of which Hooke
must have seen when he succeeded Oldenburg. But
Halley did all he could to prevent a scandal, and
finally Newton inserted into his book a statement that
the inverse square law had been deduced from Kepler's
third law of planetary motions by himself, and inde-
pendently by Wren, Hooke and Halley.
This further unpleasantness in respect to scientific
work caused Newton much pain and he wanted to
suppress Book III, "De Mundi Systemate," containing
direct applications of the inverse square law to planet-
ary theory, lunar theory, the theory of comets, tides,
etc. Fortunately, Halley's good sense succeeded in
preventing such a calamity, and Newton proceeded
with the plans originally made. On July 6, 1686, the
imprimatur, or license to print the book in the name
of the Royal Society, was given by the then President,
the famous diarist, Samuel Pepys, and within a couple
of weeks the work of printing Book I began. Book II
reached the Royal Society in March, 1687, and Book III
in April of the same year.
THE GRAVITATIONAL DECADE, 1678-1687 97
Newton's work at the " Principia " was interrupted
by an event of political importance. The accession to
the throne of King James II was soon followed by an
attempt on the part of the King to favour his fellow
Catholics in violation of the law of the land. If we
can now look with more detached eyes at this exercise
of the royal will, and admit that religious tests of any
kind are to be condemned, and acts of exclusion against
any church are equally undesirable, we cannot treat
the King's attempt to force his will upon the univer-
sities in the same way. A university is a living
monument to knowledge and truth, the degrees and
diplomas awarded by a university can be granted only
on proof being supplied of learning or research on the
part of the candidates for such honours. The only
persons qualified to judge the fitness of candidates are
the professors of the university : deprive them of this
monopoly, infringe in any way upon their free and
unfettered decision in academic matters, and the
prestige of the honours awarded at their hands is
lowered and the university loses in status and dignity
as the repository of knowledge.
James had already forced the University of Oxford
to accept as a high academic official a man who had
no qualification for occupying such a post, but who
was a Roman Catholic and as such was a nominee of
the King's. In February, 1687, the blow fell upon
the University of Cambridge. The particular form
that the King's attack took would leave us cold
nowadays, since it really amounted to removing
restrictions against Catholics as such. But the prin-
ciple at stake was one that overshadowed the actual
issue in the dispute. The Vice-Chancellor of the
University declined to carry out the royal mandate
to confer the degree of M. A, upon a certain Benedictine
monk without his taking the oaths of allegiance
and supremacy. Finally, the Vice-Chancellor was
98 SIR ISAAC NEWTON
summoned to appear before the High Commission
Court at Westminster, accompanied by representatives
of the Senate of the University. Newton was one of
the eight representatives chosen for the purpose, and
he maintained a firm determination not to submit and
not to accept any compromise.
The infamous Judge Jeffreys presided over the court.
The Vice-Chancellor was soon reduced to silence ; the
other deputies were forbidden to say anything in defence
of the attitude of the University, and ordered out of
court. " As for you/' said Jeffreys to them, " most
of you are divines. I will therefore send you home
with a text of Scripture, ' Go your way and sin no
more, lest a worse thing happen to you/ " The greatest
man of the century, not a " divine/' was among the
Cambridge representatives thus insulted, the man who
was just then putting the finishing touches to the book
that will outlive scores of royal bullies like James, and
foul-mouthed brutes like Jeffreys. The Vice-Chancellor
was not only deprived of his office, but also lost his
post as Master of Magdalen College, although the
University ultimately succeeded in its resistance.
Newton went back to his rooms between the great
gate and the chapel at Trinity and proceeded with the
proof reading and other tasks in connexion with the
publication of the " Principia." Within two months
of Newton being ejected ignominiously from the court
presided over by Jeffreys, the " Principia " was
published, dedicated to the Royal Society " flourishing
under his august Majesty James II " !
Newton was then forty-four years of age. He had
spent over twenty years in the pursuit of truth, mainly
in optics and in gravitation theory. He had remained
a bachelor, possibly by inclination ; but certainly in
accordance with the peculiar traditions that were in
force till only half a century ago, and which prevented
a college fellow leading the normal life of a human
THE GRAVITATIONAL DECADE, 1678-1687 99
being. He had remained poor in accordance with the
general practice of civilized humanity, that is content
to let its men of genius give their all to humanity and
receive nothing in return. Newton had reached middle
age in a state of semi-obscurity, known to the few like
Halley, Wren, Huygens, Leibnitz and Hooke, but un-
recognized by the masses whose adulation is blindly
bestowed and equally blindly withheld.
On the evidence of his relation, assistant and
amanuensis, Humphrey Newton of Grantham, who
was with Isaac Newton from 1683 to 1689, we know
that Newton was " very meek, sedate, and humble,
never seemingly angry, of profound thought, his
countenance mild, pleasant, and comely. f ' He delivered
his lectures to the few who cared to hear them, dictating
for half an hour as rapidly as his audience could write ;
and if nobody came he went back to his work. He took
no recreation or had any pastime, devoting all his time
to his work. " He ate very sparingly, nay, ofttimes
he has forgot to eat at all, so that, going into his
chambers, I have found his mess untouched. ... He
very rarely went to bed till two or three of the clock,
sometimes not till five or six, lying about four or five
hours, especially at spring and fall of the leaf, at which
times he used to employ about six weeks in his elabora-
tory, the fire scarce going out either night or day, he
sitting up one night and I another, till he had finished
his chemical experiments.
" I cannot say I ever saw him drink either wine, ale,
or beer, excepting at meals, and then but very spar-
ingly. He very rarely went to dine in the hall, except
on some public days, and then if he has not been
minded, would go very carelessly, with shoes down of
heels, and his head scarcely combed. ... He was
very curious in his garden, which was never out at
order, in which he would at some seldome time take a
short walk or two, not enduring to see a weed in it."
100 SIR ISAAC NEWTON
This garden was the space between the road and the
college on the right-hand side on entering the great
gate at Trinity College, and contained his chemical
laboratory. " In his chamber he walked so very much
that you might have thought him to be educated at
Athens among the Aristotelean sect. ... He kept
neither dog nor cat in his chamber." This disposes of
the well-known story that Newton made a hole in the
door for his cat to get in and out without disturbing
him, and then when the cat had kittens, made another
and smaller hole for the kittens to get through !
Newton's refusal to go into holy orders is illuminated
by the following : "He very seldom went to Chapel,
that being the time he chiefly took his repose ; and,
as for the afternoon, his earnest and indefatigable
studies retained him, so that he scarcely knew the
house of prayer. Very frequently, on Sundays, he
went to St. Mary's Church, especially in the fore-
noon. ... As for his private prayers I can say
nothing of them ; I am apt to believe his intense
studies deprived him of the better part." But busy
as Newton might be he had time for charitable deeds,
and " few went empty handed from him." He helped
poor relations and neighbours most generously, tipped
the college porters frequently, although he never broke
their rest by coming in late at night. He was patient
and conscientious an eminent example of the great
worker prosecuting his studies quietly, and little
dreaming that his discoveries were to become the
glory of mankind.
THE "PRINCIPIA," 1687
Nec fas est propius mortal! attingere divos.
THE "Principia" appeared in July, 1687, in
one small quarto volume containing 500 pages.
It was illustrated with a large number of
diagrams in the form of woodcuts, was issued bound in
calf, and was sold at nine shillings per copy. Halley's
generosity to and admiration for Newton are both
apparent from the following, taken from a letter
written by the former on July 5, 1687 : " I have
at length brought your book to an end, and hope it
will please you. The last errata came just in time
to be inserted. I will present from you the book
you desire to the Royal Society, Mr. Boyle, Mr.
Paget, Mr. Flamsteed, and if there be any else in
town that you design to gratify that way ; and I have
sent you to bestow on your friends in the University
20 copies, which I entreat you to accept. ... I hope
you will not repent you of the pains you have taken in
so laudable a piece, so much to your own and the
nation's credit, but rather, after you shall have a little
diverted yourself with other studies, that you will
resume those contemplations wherein you had so great
success, and attempt the perfection of lunar theory,
which will be of prodigious use in navigation, as well
as of profound and public speculation."
In view of King James II having been Lord High
102 SIR ISAAC NEWTON
Admiral early in his brother's reign and the probable
value of Newton's work in navigation, a copy of the
" Principia " was presented to the King by Halley.
Did James make much use of it in his many voyages
across the sea after his indignant subjects had driven
him out of the country sixteen months later ?
The great classics of science are rarely read in sub-
sequent generations. Whereas the young school boy
or girl is introduced to Milton's work in the original,
and learns, if judiciously taught, to admire and per-
haps to emulate the great lines of our incomparable
national poet, no boy or girl at school ever sees a copy
of the book written by his junior contemporary,
Newton. We do not blame modern educationists
for preferring modern books on mathematics and
science as text-books for modern pupils. The con-
tinued progress of science forces us to modernize, to
condense and to systematize the mathematical and
scientific knowledge of the past in a manner suitable
for the consumption of present-day learners. Yet one
would wish that a little time could be found to introduce
the pupils of our schools, and especially of our univer-
sities, to the actual words of the great original thinkers
in science. If scientific results are impersonal and
objective, scientific research embodies the mind, the
soul, of the worker, and the essence of education is
surely the bringing to bear upon one mind the influence
of another mind, a forerunner in the search for
The " Principia " was written and issued in Latin,
the international language of learning till a few genera-
tions ago. Newton was not only a discoverer of
unique power, but also an elegant exponent of his
views. Said Laplace, the great scientific representa-
tive of a different and of a hostile nation : "... tout
cela pr6sente avec beaucoup d'elegance, assure a
Touvrage des Principes, la preeminence sur les autres
THE " PRINCIPIA." 1687 108
productions de 1'esprit humain " extreme but not
The " Principia " is not a compendium of knowledge
reproducing the learning of the past with original
touches here and there. It is one of the most
consistently original books ever written. The funda-
mental laws of mechanics are here formulated for the
first time, the mathematical ideas required in the
arguments are those invented by the author himself,
the forces invoked to explain the motions considered
are those arrived at by the author's own intuition,
the phenomena explained had never been satisfactorily
accounted for before, the problems initiated have since
occupied the best minds of humanity for two centuries
and a half, the results deduced have been the admira-
tion of successive generations of astronomers and mathe-
maticians and pervading the book there is a spirit of
dignity and simplicity, a sanity of outlook, a soberness
of expression, and a grandeur of conception, that place
both the author and his work on an unequalled level
of eminence. Immortals themselves, Halley and La-
place could appraise at its true value genius superior
to their own.
It is quite impossible to convey an adequate impres-
sion of Newton's achievements in the " Principia " in
a brief space and in non-technical language. A mere
enumeration of the topics discussed is sufficient to
impress with wonder and admiration one so versed
in the subjects of mechanics and astronomy as to
appreciate the importance of these topics. First there
is an introduction, in which, after some definitions and
the consideration of the meaning of space and time,
Newton formulates the three laws of motion that are
still called by his name, with deductions and applica-
tions of interest and significance.
We have already stated how significant for the
development of dynamical astronomy were the
104 SIR ISAAC NEWTON
dynamical experiments of Galileo ; without them the
whole subject was quite unapproachable. Newton
therefore gives in the " Principia " a clear statement
of the laws of motion deduced from these experiments.
The first two laws have already been mentioned,
namely, that the absence of force implies uniform
motion in a straight line, while change of motion or
acceleration is determined by force. A third law must
now be added : its importance in connexion with our
present subject is hardly ever explained adequately,
whereas without it Newton's work would have been
The third law of motion is the famous statement
that action and reaction between two bodies are
always equal and opposite. We can readily see the
importance of this law in Newton's train of thought.
Newton's use of the principles of dynamics was in
itself a lesson in their clarification and of their sig-
Astronomical progress from the flat earth to the
spherical earth and from the fixed spherical earth to
the- earth as a rotating and revolving planet, implied
more than this bald statement seems to convey.
The human intellect needs an anchorage in space and
time as much as it needs one in its spiritual life. This
was found in the flat earth. Man was banished from
the flat earth and sent to wander in bewilderment
round the surface of a sphere. Still, he had the
centre of the earth, the fixed centre of all things.
Copernijps completely banished man's intellectual
anchorage from the earth and sent it to the sun.
Humanity struggled against the decree of banishment,
but finally and with a bad grace it submitted, and
promptly appropriated the centre of the sun as the
fixed point, the hub of the universe, the centre of all
creation. Kepler's discovery of the more accurate
paths of the planets left this state of affairs unchanged
THE "PRINCIPIA," 1687 10T
the sun remained enthroned in mighty splendour at
the centre of the universe, directing his vassals, the
planets, and their satellites.
Meanwhile Galileo discovered the laws of dynamics.
When we discuss motion, especially variations in
motion, we necessarily look for a comparison point.
When we say that a body is at rest we cannot mean
anything else than that it is not changing its position
relative to a set of bodies which we take to be the
standard. Is the reader at rest while reading this
page ? Is he reading this book in his house seated
quietly near the fire or comfortably in bed ? He is
clearly at rest yet he is being dragged round with
the earth's diurnal rotation and with the earth's
annual revolution. What then shall be our standard
of rest in dynamics ? To which body are we to refer
motions in order to decide whether they are uniform
or varying, and what the variations are ?
It is a remarkable feature of natural phenomena
that in spite of their apparent complexity, Nature
always contrives to make our researches into her
secrets amenable to our limited intellectual powers.
Galileo carried out his experiments on the earth he
ignored the earth's motion completely. The effects of
the earth's motion on his experiments were negligible,
because the earth's angular rates of rotation and
revolution are both so small as to produce no appreci-
able effect on ordinary terrestrial dynamical phenomena.
These and other considerations made it possible for
Galileo to arrive at correct conclusions about the
earth's gravity, and about the effects of forces on
bodies. Would we even now be in possession of
reasonable views on dynamics if the earth were a very
small body, say ten miles in diameter, or if it rotated
on its axis once in ten minutes, or revolved round
the sun once in twenty-four hours ? The phenomena
of solar and terrestrial gravitation would be so
?06 SIR ISAAC NEWTON
confounded together, as well as with variations in the
earth's gravity itself, that no rhyme or reason could
have been discovered in the subject by finite intel-
ligences. Let us be grateful to a kindly Nature for
presenting her problems to us step by step, and not
confounding us with a too precipitate confrontation
of all her complications.
Galileo could take the earth as his "dynamical
standard ; in fact, the surface of the earth wherever
he happened to be was good enough for his purposes.
This would of course be absurd in dealing with extra-
terrestrial dynamics. People still take the sun as
dynamical standard, and we often hear loose talk about
the sun being fixed at the centre of the solar system.
But Newton had to postulate universal gravitation,
that all bodies attract one another the sun pulls the
planets and the planets pull the sun, the earth pulls
the moon and the moon pulls the earth ; it were there-
fore ridiculous to imagine the sun " nailed down "
and not yielding at all to the attractions of all the other
bodies in the solar system. For this problem Newton
used the third law of motion. Let the sun and earth
attract one another, but let the force of attraction
exerted by each on the other be the same, yet in
opposite directions. The accelerations produced will
be inversely as the masses, and it is at once seen that
the point which divides the distance between the centre
inversely as the masses will in fact have no accelera-
tion at all ! A little mathematical reasoning enabled
Newton to extend this to the whole solar system ;
the centre of gravity of the whole solar system has no
What about the so-called fixed stars ? Do they
attract ? Why not ? Of course they do. Then there
are external forces on the bodies of the solar system,
and its centre of gravity has not zero acceleration.
We have here once more an example of the benignity
THE " PRINCIPIA," 1687 107
of Nature towards human scientific research The
stars are indeed so far off that Newton made no serious
error in neglecting the accelerative effect of their
gravitational pulls. He had no real knowledge of
the distances of the stars, but the intuition of genius
stood him in good stead.
Newton thus took the centre of gravity of the solar
system to have no acceleration. The logical thing
would be to say that it has a uniform speed in a
constant direction. But Newton had no means of
discussing the motion of the solar system as a whole
this came over a century later. He therefore took a
deep plunge and as we shall see later he made the centre
of gravity be at rest. It was left to the nineteenth
century to correct this, and to the twentieth century
to draw far-reaching conclusions from the correction.
One of the most interesting features of the " Prin-
cipia " is this continual provocation of thought on
the part of the reader. The main theorems and pro-
positions are given in clear, brief, crisp and conventional
language. The implications of the theorems are dis-
cussed in corollaries, and particularly in the " Scholia."
A scholium is a general remark or conclusion that
Newton often appends to some particularly important
proposition and set of propositions. The scholia
contain a vast amount of stimulating discussion, and
they shed a large amount of light upon the whole
subject, by means of the citation of authorities,
experimental investigations and results, and any-
thing else that helps to illuminate the matter in
The main work is in the two books of the " De
Motu Corporum " and in a third book on " De Mundi
Systemate." Book I (the first part of " De Motu ")
commences with a brief account of the principles of
the method of fluxions the first printed statement
of this discovery ever issued by Newton. We have
108 SIR ISAAC NEWTON
already seen that Newton had written brief treatises
on fluxions about twenty years before. His dis-
coveries in this field were communicated in manuscript
to several mathematicians, and some correspondence
with Leibnitz had taken place as far back as 1676.
Eight years later Leibnitz published in the " Acta
Eruditorum " a mathematical journal edited by
himself at Leipzig in Saxony an account of the
differential calculus, essentially the same method as
fluxions, but with a different and in fact more suitable
notation, giving an oblique reference to Newton's
work of a similar kind. Leibnitz developed the
subject further in another paper two years later,
1686. No doubt Newton read these papers and felt
that the time had come when he should give to the
world his own theory of fluxions. He accordingly
incorporated in the " Principia " a section on this
subject, in the form of eleven lemmas or preliminary
propositions required for the sequel. The treatment
is very brief, and even at this late hour twenty-one
years after his developing the method the notation
is not given ; this was not printed till six or seven
years later in the works of John Wallis ! Meanwhile
Leibnitz' method and notation were being used on
the Continent with phenomenal success for solving
difficult and important problems.
After this preliminary, Newton attacks the motion
of a body under an attraction directed to a fixed point.
When the path is a conic section the force must bear a
certain relation to the distance this is discovered,
and then particularized for the case where the centre
of attraction is at a focus of the conic, when the law
is that of the inverse square of the distance. Detailed
developments of this type of motion follow, and Newton
examines the way in which any particular orbit is
described, showing how to find the position at any
THE " PRINCIPIA," 1687 109
This would suffice for the discussion of the planetary
motions in accordance with Kepler's third law. But
Newton did not merely attribute gravitational pro-
perties to the sun as acting on the planets or to the
earth as acting on the moon. It soon became clear to
him, especially on the basis of his third law of motion,
that every heavenly body attracts every other heavenly
body, that our earth attracts and is attracted by the
moon, that the sun attracts and is attracted by the
planets, that Jupiter attracts and is attracted by his
satellites. It is a further instance of the encourage-
ment that Nature gives to scientific discovery that the
sun is so large compared to the planets, containing
about a third of a million times as much matter as the
earth, indeed about eight hundred times as much matter
as all the planets put together, and further that the
planets are very far apart. The result is that it is
permissible in discussing the motion of any one planet
to omit the pulls exerted upon it by the other bodies
in the solar system, and to assume that it moves under
the sun's influence alone. The same applies to a
satellite. Satellites are usually so close to the planets
round which they revolve, that even the sun's distur-
bance can be neglected, at least as a first approximation.
Again we might ask ourselves what progress in astron-
omy would have been possible if, say, the planets had
masses which were considerable fractions of the sun's
mass, or if two planets came occasionally very close
together, or if our moon were very much further away
from the earth than it actually is.
The problem of the sun and one planet, of a planet
and one satellite, was the problem discussed by
Newton primarily. But he had to go to a second
approximation in order to explain a number of
irregularities observed in the motion of the moon,
and known for centuries. Newton's law of uni-
versal gravitation suggested what had not yet been
110 SIR ISAAC NEWTON
discovered, namely, that even Kepler's laws were only
approximately correct. Happily, Kepler lived at a
time when these mutual disturbances or perturbations
of planets were not measurable instrumental accuracy
had not risen to this level. He could therefore deduce
the elliptic motion round a focus without being troubled
by the occasionally quite considerable deviations there-
In the case of the moon the disturbances were so great
as to have been observable long before Tycho Brahe,
Kepler and Newton. The moon thus presented an
excellent means of testing not only the first rough
results of Newton's theory, but also its more accurate
consequences. The preparation for this is contained
in the next section of Book I, where Newton discusses
the effects of any law of force, the case of paths which
are not closed, so that the moving body does not
return to its original position exactly, as well as of
A very important and fundamental theorem now
follows. Newton was not content to attribute gravita-
tion to the sun as a whole, or to any body like the
earth or moon as a whole. He sought to discover the
gravitational effect of any body on the basis of allowing
each particle of the body to attract for itself, in which
case, of course, it cannot be guessed off-hand what the
total effect would be, even in such a simple case as a
sphere the really important case in astronomy. In
a singularly beautiful manner Newton proves that if
the matter of a sphere is arranged symmetrically
round the centre it produces at any outside point the
same force as if all the mass of the sphere were con-
centrated at the centre of the sphere.
What was the use of this theorem ? Could not
Newton say that this is the law which he postulates,
since heavenly bodies are spheres ? Newton knew,
however, that in this consideration of the attraction
THE " PRINCIPIA," 1687 111
produced by the separate particles of a body he had
the key to many mysteries the flattened shape of
the earth, precession, tides, etc. Some theorems on
the attractions produced by non-spherical bodies
follow, and Book I comes to an end with a somewhat
irrelevant discussion of motions that refer to Newton's
conception of light as due to tiny corpuscles moving
with great speed this last piece of work is now entirely
out of date and discarded.
Book II of " De Motu Corporum " deals with the
problem of motion in a medium of some kind which
might produce a resistive effect to the motion. New-
ton takes this resistance to be proportional first to
the velocity, and then to the square of the velocity ;
finally he takes the resistance to be in two parts, one
proportional to the velocity and the other to the
square of the velocity thus anticipating in remarkable
manner modern ideas on air resistance in aeronautics.
The results are then applied to motions under central
attractions where resistance of this kind exists, and
interesting results in the form of spiral motions de-
This leads Newton to the consideration of fluids in
general and their equilibrium under gravitational
attractions a subject which has become of great
importance in connexion with the discussion of the
shapes of heavenly bodies. Since the pendulum is
important in measuring the force of gravity at the
earth's surface, Newton examines the motion of a
pendulum in a resisting medium like air, and naturally
proceeds to discuss the way in which the resistance
depends upon the size and shape of the bob of the
pendulum, upon the density of the medium, upon the
velocity, etc. The study of wave motion in fluids comes
next, and the velocity of propagation of such a wave
is obtained by Newton, with obvious application to
the propagation of sound through air. Experimental
112 SIR ISAAC NEWTON
verification was attempted in that famous walk in
the cloisters of Neville's Court at Trinity, where the
modern don or modern undergraduate never fails to
test the quadruple echo which Newton claims to have
heard there. Experimenting in this walk Newton
measured the velocity of sound roughly, with qualita-
tive if not quantitative verification of his mathematics.
One further point had to be settled before Newton
could proceed to the application of his theory to the
solar system. The Cartesian theory of vortices was
then the accepted view of the cause of the motions of
the planets. This theory had to be demolished first,
and Newton disposed of it in a few simple propositions.
He first shows that if the vortices exist and persist
then they must be such that the fluid in each vortex
rotates as a whole, as if it were one rigid body, with-
out differential angular motions. It follows that the
further a point is from the axis of the vortex, the
faster it moves, so that the vortex theory gives velocities
to the planets which are in complete contradiction to
the observed velocities, the planets being known to
move faster when nearer the sun and slower when
farther away from the sun. " Hence the Vortex
Theory is in complete conflict with astronomical facts,
and so far from explaining celestial motions would tend
to upset them/'
The stage is now set for the final scene, the recon-
struction of the phenomena of the solar system by
means of the law of universal gravitation. Book III,
" De Mundi Systemate," the book that Newton was
for suppressing when worried about Hooke's claims to
prior discovery, shows us Newton at the very pinnacle
of his intellectual achievement. Here we see him as
if he were a creator conjuring up before our charmed
vision whirling and rotating planets and satellites,
flowing and ebbing tides, erratic wanderings of
THE " PRINCIPIA," 1687 113
A brief preface in the form of " Hypotheses "
contains two statements that throw a brilliant light upon
the scientific character of Newton's thought. Right
through the Middle Ages all thinkers differentiated
somehow between earthly and celestial phenomena,
postulating mystical causes and effects which bore
little if any relation to ascertained facts. Newton
broke with this most forcibly. " Like effects in nature
are produced by like causes/' he asserted, " as breathing
in man and in beast, the fall of stones in Europe and
in America, the light of the kitchen fire and of the
sun, the reflection of light on the earth and on the
planets." Thus was humanity finally redeemed from
the bondage of many centuries to belief in the per-
fection of the heavenly, imperfection of the earthly,
and all phenomena were reduced, or raised, to the
same level of rational causality.
It is interesting that Newton takes as his first proof
of the inverse square law the fact that the periods and
distances of the satellites of Jupiter and Saturn follow
Kepler's third law, i.e. the squares of the periods are pro-
portional to the cubes of the mean distances. Why
does not Newton give the case of the moon first ?
We have here another illustration, perhaps, of Newton's
preference for the immediately visible, Anybody can
verify the relationship between the periods and
distances of the four large satellites of Jupiter not
much observation is needed ; whereas the case of the
planets round the sun needs careful measurement,
and the case of the moon is a somewhat recondite
application of dynamical principles, not well under-
stood by many men in Newton's day.
Having established the gravitation of Jupiter, Saturn,
the sun and the earth, Newton then leads on to the grand
generalization of the law of universal gravitation, the
force between two bodies being proportional to the
product of their masses, and inversely proportional
114 SIR ISAAC NEWTON
to the square of the distance between them. He
shows that no appreciable resistance is experienced
by the planets so that their motions may be expected
to go on indefinitely. He then determines the motion :
the centre of gravity of the sun and all the planets
is at rest a great improvement on the Copernican
system in which the centre of the sun was taken to be
at rest the sun never receding much from this point,
while the planets move round the sun in ellipses, with
a focus of each ellipse at the sun.
Newton establishes the uniform rotations of the
planets by reference to the moon's librations, already
mentioned here, and then proceeds to discuss the shape
that a planet should assume, using the knowledge of
the apparent flattening of Jupiter at its poles, as told
him by Cassini of Paris and Flamsteed of Greenwich.
He proves that the rotation of a planet will cause such
flattening, and discusses pendulum observations in
the case of the earth to show that the variation in the
earth's gravitation from place to place on its surface
is explainable by this flattening.
The flattening of the earth explains the precession
of the equinoxes, a phenomenon known since the middle
of the second century B.C., and completely misunder-
stood till Newton gave it its natural explanation.
Since the earth is not an exact sphere, the attractions
exerted upon it by the sun and by the moon do not
pass through the earth's centre, but meet the earth's
axis at some little distance away from the centre.
The effect in each case is to produce a turning effect,
or moment, about an axis lying in the equatorial
plane of the earth ; this gives a gyroscopic or top
motion, in which the axis of the earth describes a
cone in the heavens. This is one of the most beautiful
deductions from Newton's theory that can be imagined,
and the agreement quantitatively leaves little to be
THE " PRINCIPIA," 1687 115
Having shown in considerable detail that the
irregularities observed in the motions of the moon and
of the satellites of Jupiter and of Saturn (the only
secondary bodies then known) can be explained by
SUN OR MOON
"I ECCENTRIC UNE OF GRAVITATIONAL PULL EXERTEOON
EARTH (DUE TO FLATTENING)
CAUSE OF PRECESSION
Pull of sun or moon on earth does not (owing to flattening of the earth) pass
through its centre, as shown here. A torque is produced about an axis through
the earth's centre perpendicular to the plane of the paper. This causes the earth's
axis to " precess," like a top, in the reverse sense to the earth's own rotation.
gravitation as due to the perturbative effect of the sun,
Newton proceeds to the question of tides. He at once
attributes the tides to the differential gravitative effects
of the sun and moon. If we consider the earth and
the moon, the former containing on its surface a flowing
SIR ISAAC NEWTON
substance like water, we see that the attraction
produced by the moon on unit mass of the water on the
side of the earth away from the moon must be less than
on unit mass on the side towards the moon, while on the
earth itself the attraction corresponds to the total mass
of the earth concentrated at the centre of the earth,
and thus per unit mass produces effects lying inter-
mediate between those on the further and nearer
waters. The result is that the nearer waters are
dragged towards the moon more than the earth as a
Gravitational pulls of Sun and Moon on Tides due to sun and moon respectively.
Earth, and on waters on near side and on
far side of Earth.
whole, and the further waters are dragged towards
the moon less than the earth as a whole. The waters
are thus heaped up on the two sides of the earth,
towards the moon and away from the moon.
The same applies to the sun. But the moon is so
near that its tidal effect is greater than that of the sun ;
hence the tides follow the moon as a whole. Hence,
also, we get the very high tides at new and full moon,
when the sun and moon reinforce one another's tidal
THE " PRINCIPIA," 1687 117
effects, and low tides at the quarters, when the sun
and moon tend to neutralize one another's tidal effects.
Finally we get a rational and beautiful treatment of
comets. Newton's knowledge of comets was some-
what scanty when he discussed them with Flamsteed
several years before he wrote this theory. But in the
" De Mundi," he produces a remarkable account of
the subject. He proves that comets must move in
PATH OF PERIODIC COMET
Long ellipse with one focus at the centre of the sun.
interplanetary space and shows that they also move in
conies about a focus. Kepler's ellipses were one type
of conic the cometary paths ate another type,
vindicating wonderfully the generality of Newton's
gravitational ideas. Newton then reverts to the
parabola as an approximation to a long cometary
ellipse, and discusses how to find the approximate
parabolic path of a comet from three observations of
its position as seen from the earth a result of funda-
mental importance, since by its means one can deduce
the future path of a comet quickly after its first
appearance, so as to facilitate observation and a more
accurate determination of its path subsequently.
118 SIR ISAAC NEWTON
There is much in the " Principia " to which we have
not referred and which is of great importance in the
theory of the heavenly motions . We have talked about
the masses of the planets and of the sun. How can
we find these masses ? - Nothing is simpler when we
have once grasped the fundamental idea of gravitation.
If a planet has a satellite, then by the motion of the
satellite we can calculate the gravitative effect of the
planet at the distance of the satellite. But we have
the gravitative effect of the sun for all sorts of dis-
tances. By comparison we get the ratio of the gravita-
tive effects of the sun and of the planet for the same
distance, and this is the ratio of their masses. In this
way Newton could find the ratio of the mass of the sun
to that of the earth or of Jupiter. Now we can find
this ratio for all the planets in this way, except Mercury
and Venus which seem to have no moons.
No limit can indeed be foreseen to the developments
consequent upon Newton's work. The " Principia "
is not an ordinary book which plays its part in the
progress of knowledge and then disappears. Its
theorems and methods, principles and laws, are pro-
nouncements that humanity has studied for genera-
tions. Over and over again the greatest triumphs
of human thought have been achieved as the direct
consequence of Newton's genius. The exact working
out of the motions of the bodies in the solar system at
the hands of Laplace, Lagrange and their successors
has introduced into astronomical prediction such a
degree of precision that popular concern is aroused
when an eclipse takes place a couple of seconds earlier
or later than the time calculated in advance, and
messages are cabled round the world to announce this
fact. The slight differences between the observed
motion of Uranus and that calculated on the basis
of the sun's attraction and the perturbations due to
the known planets, led to the discovery on paper by
THE " PRINCIPIA," 1687 119
mathematical calculation of the till then unknown
planet Neptune. The difference between the motion
of Mercury and that deduced from theory has been one
of the main planks in Einstein's platform. And what
is perhaps the outstanding event in the science of our
own generation the theory of relativity is a wonder-
ful vindication of the sagacity of the originator of
universal gravitation, for it is the universality of
gravitation that is the chief argument in Einstein's
view, and the universality of gravitation is the dis-
tinctive characteristic of Newton's conception of this
But one of the most historic vindications of Newton's
genius was coupled with that of none other than his
friend and admirer Halley. Man is always impressed
with the power of foretelling events yet to come, and
Halley was able to present to the world a remarkable
piece of prophecy, the fulfilment of which was left
to the generations that came after him and made him
one of the immortals of astronomy.
A great comet had appeared in 1682, and Halley
had observed it carefully, deducing its path when near
the sun. When Newton published the " Principia "
and demonstrated that long elliptic paths with a focus
at the sun are possible, he concluded that what appears
to be a parabolic path of a comet may really be a long
elliptic path, and suggested that the periodic time of a
comet moving in a long ellipse could be ascertained by
its return after a long interval of time. But a comet
becomes visible to us only when it is near the sun,
whose effect is to eject matter from the comet ary
nucleus in the form of one or more tails. Thus a
comet is invisible except for a very short time when
it is near the sun, and a comet could not be traced
all round its elliptic orbit in order to verify Newton's
The sagacity of Halley came to Newton's help.
120 SIR ISAAC NEWTON
Halley set himself to examine all reliable observations
of comets that had appeared in the past, and
where sufficient material existed he calculated the
parabolic path which Newton took to be the
first approximation. He discovered that in the year
1607 a comet had been observed whose approximate
parabolic path was very nearly identical with that of
1682. This was interesting as a coincidence, perhaps.
But Halley found that in the year 1531 a comet had
been observed whose approximate parabolic path was
also nearly identical with that of 1682 further, the
interval 1531-1607 is nearly the same as the interval
1607-1682. Halley became convinced that this was
not a cometary accident or coincidence, but rather a
cometary habit, and concluded that he had indeed
discovered a periodic comet, the existence of which
was suggested by Newton. Any deviations from exact
identity of the calculated parabolas, and any inequality
between the two intervals, Halley attributed to
Newton encouraged Halley in this view, and in
1705 Halley announced that the comet he had observed
in 1682 would reappear after suffering severe per-
turbation owing to a very near approach to Jupiter
about the end of 1758 or the beginning of 1759. Halley
had looked back into the centuries and observed the
similarities of the cometary paths of 1531, 1607 and
1682 ; he looked forward, with the aid of Newton, into
generations to come and saw his comet wending its
long and lonely way, past the orbit of the earth, past
the orbit of Mars, past Jupiter, past Saturn, deeper
and deeper into space. Halley and Newton grew older
and older. Newton passed away and Halley was left
to continue alone the dynamical watch of the comet.
He rewrote his prediction, and, feeling that he would
never see the year of the comet's return, expressed
the hope that if the comet did come back as predicted
THE " PRINCIPIA," 1687 121
" impartial posterity will not refuse to acknowledge
that this was first discovered by an Englishman. 1 '
Within a month of the time given by calculations
based upon Newton's laws the comet reappeared.
Halley was dead, but grateful posterity will forget
neither Halley's personality nor his nationality.
Halley's Comet reappeared in 1835 and in 1910, in
better and better agreement with calculated time and
place a lasting monument (not permanent since
comets disintegrate, and Halley's Comet is believed
by some to be showing signs of decay already) to the
memory of Newton and Halley. It is exceedingly
appropriate that Halley's memory should have thus
become linked with that of the man whom he admired
so selflessly and encouraged with such devotion.
Such are the contents of the " Principia " as issued
in 1687, written by the man driven out of his court
by Jeffreys and admonished to mend his ways, and
printed at the personal expense and risk of the man
who could best appreciate its contents.
THE TRANSITIONAL DECADE, 1687-1696
Has matter more than motion ? Has it thought,
Judgment and genius ? Has it framed such laws,
Which, but to guess, a Newton made immortal ?
EDWARD YOUNG : " On the Being of a God "
EVERY new idea has to overcome prejudice
and mental inertia. The publication of the
" Principia " was a turning point in the in-
tellectual history of mankind ; yet Newton came on
the scene when Descartes' vortex theory had become
well entrenched, enjoying the prestige associated with
the immortal name of this philosopher and mathe-
matician. On the Continent, in fact, Newton's theory
made little progress for some time. The supposed
suggestion of action at a distance, without any hypo-
thesis as to how the action was propagated in the
intervening space, caused considerable opposition on
the part of Leibnitz and others, especially when
personal jealousies confused^he issue. It will already
be clear to the reader that ^ewton was the last man
in the world to postulate non-physical or anti-physical
conceptions ; he did indeed make an attempt at a
physical explanation of gravitation based upon the
jetherji But this effort produced nothing really useful,
and more than two centuries had to elapse before a
satisfactory view of gravitation began to emerge.
Things were better in England, where Newton's
work found ready approval among those few whose
opinions were worthy of consideration. Within three
THE TRANSITIONAL DECADE, 1687-1696 123
years of the publication of the " Principia " its
contents were taught at Cambridge, St. Andrews and
Edinburgh, while Oxford followed suit before very
long. The " Principia " helped to establish mathe-
matical studies on a firm basis, especially at Cambridge.
Non-mathematical thinkers took special pains to study
the physical portions of the book, and the influence of
Newton's ideas spread quickly among the best minds
of the day. The " Principia " sold quickly, and one
hopes that Halley did not lose on his generous trans-
action. Copies of the first edition became scarce, and
people paid four or five times the original cost for a
copy. One case is known of a Scotsman who wrote out
the whole book by hand, as he could not get a copy
at a reasonable price.
Following Halley's advice Newton took a rest from
scientific work. In November, 1688, William of
Orange landed at Torbay and marched upon London.
James II fled the country and William was invited to
share the throne with his wife, James 1 daughter,
Mary II. In January, 1689, the so-called Convention
Parliament was summoned to Westminster, and, as
Macaulay says : " Among the crowd of silent members
appeared the majestic forehead and pensive face of
Isaac Newton ... he sate there, in his modest great-
ness, the unobtrusive but unflinching friend of civil
and religious freedom." Parliament did not hear
Newton's voice in debate during the thirteen months
that he served as M.P. for Cambridge University
, till the dissolution in February, 1690 yet Newton's
presence was not unfelt. He was a keen supporter of
the new royal house and a Whig in politics, being a
strong believer in religious toleration, and a stout
opponent of all forms of oppression in particular
of the oppression, religious and otherwise, practised
by the Stuarts. He did much to make and keep
Cambridge loyal to King William and Queen Mary.
124 SIR ISAAC NEWTON
Newton's presence in London served to accentuate
the unsatisfactory nature of his own personal position.
He was nearly fifty years of age, and he had spent all
his manhood days in the most unremitting scientific
toil. No recognition of a tangible nature had come
to him. He was still college fellow and university
professor, conscious of a harrowing poverty, which
narrowed his existence and prevented him from
satisfying the needs of his relations and other depen-
dents, and which had necessitated his acceptance of
Halley's offer to shoulder the financial responsibility
involved in printing the " Principia."
Locke, Pepys and other friends of Newton who
occupied prominent positions in public life tried to
secure for him some public post worthy of his great-
ness. In particular, Charles Montague, an intimate
friend of Newton's and a fellow-member of the Con-
vention Parliament, who was rising quickly in the
political firmament, did all he could for him. But the
great men of the day were too busy to bother about a
mathematician whose work they could not under-
stand. When the post of Provost (or Head) of King's
College, Cambridge, fell vacant, Newton was nomi-
nated, but ultimately failed to secure appointment
because he was neither a Fellow of King's nor in
priest's orders. The dissolution saw Newton back in
Cambridge, resuming his bachelor life in a college cell.
Meanwhile other things had happened to depress
Newton. During the year of his membership of the
House of Commons his mother, Mrs. Smith, became
seriously ill, and Newton left everything to minister
to her. He was a skilful nurse ; he sat up with his
mother whole nights, and did everything in his power
to lighten her sufferings. She died without having
enjoyed the satisfaction of seeing her son Isaac receive
the token of his nation's gratitude that was his
THE TRANSITIONAL DECADE, 1687-1696 125
Did his mother's death turn Newton's attention to
theology ? As early as 1690 his interest in theological
discussion began to manifest itself and was encouraged
by others. He corresponded with various people
about gravitation, and drew up for John Wallis in
1692 a few propositions on fluxions, which were
printed in the second volume of Wallis 1 works ; he
corresponded with Leibnitz about his mathematical
work ; he gave free rein to his lifelong interest in
alchemy and studied many old and contemporary
books on this subject ; he interested himself in a
method due to Boyle for making gold out of mercury ;
but one of the most important of Newton's productions
during the period 1690-1693 was in the domain of
In 1690 Newton wrote, but did not publish, a
discussion of " Two Notable Corruptions of the
Scriptures, in a Letter to a Friend." These referred to
I John v, 7, and i Tim. iii, 16, and Newton claimed
that the trinitarian interpretations of these passages
were not justified by the correct original text. It is
difficult to say whether Newton did or did not believe
in the Trinity ; at any rate, it is clear that he did not
accept all the tenets of the prevailing Church unques-
tioningly, and was as independent in theological belief
as in scientific investigation. Newton also wrote then
and later on the Prophecies of Daniel, on the Apocalypse
of St. John, and about many other religious topics.
But the most famous of his theological writings are
his letters to Bentley.
Richard Bentley was a brilliant young scholar who
afterwards became Master of Trinity. He was inter-
ested in gravitation, and Newton gave him advice on
the preliminary reading in mathematics needed in
order to be able to follow the " Principia." In
December, 1691, the famous Robert Boyle died and
left some money to endow a lectureship in the interests
126 SIR ISAAC NEWTON
of Christian orthodoxy. Bentley was appointed the
first lecturer under the bequest, and he decided to
devote two out of the eight lectures to a consideration
of divine providence as evidenced by the physical
universe. But he encountered some difficulties and
applied to Newton for help. Newton replied in four
letters, written between December, 1692, and February,
Bentley's chief difficulty was the argument used
by the Roman poet Lucretius, who had claimed that
there is no need for postulating a divine creation,
since matter evenly scattered throughout space, and
endowed with the power of gravity, would form the
universe as we know it. Newton replied that matter
in a state of diffusion could not, if left to itself, and
without the aid of Divine will and design, produce
differently constituted bodies like the bright sun and
the dark planets, and could not endow the planets with
their characteristic nearly circular motions round the
sun. Plato's idea that the planets originated very far
away and then fell inwards till they reached their
present orbits, was proved by Newton to be incon-
sistent with the law of gravitation, since it would
imply a sudden halving of the sun's attractive power
when the planets assumed their orbital motions.
Nowadays we would not take it as obvious that
diffused matter, or nebula, will not explain the forma-
tion of the solar system a nebular hypothesis has in
fact become associated with such names as Kant,
Herschel and Laplace.
Meanwhile Newton's bachelor habits began to tell
upon his health. He must have had an excellent con-
stitution, since he enjoyed a long life in spite of his
many years of irregular and insufficient sleep, and
negligence as regards food and other bodily comforts.
He became physically unwell and suffered from
nervous irritability. He began to brood over the
THE TRANSITIONAL DECADE, 1687-1696 127
injustice done him, which his experience as a member
of the House of Commons had made him feel most
keenly. Public offices of honour and of profit were
being bestowed upon the deserving and the undeserv-
ing, men whose merits were incomparably lower than
his own were playing a prominent role in the life of
England ; while he saw no prospect for himself but
the obscure and desolate life of the college recluse.
Always difficult in personal relationships, Newton did
not hesitate to charge his friends with being false to
him, and wrote some silly letters to this effect.
Newton's behaviour and unhappiness, aggravated as
he himself testified " by sleeping too often by my
fire  ... so that when I wrote to you [Locke]
I had not slept an hour a night for a fortnight together,
and for five days together not a wink/' alarmed his
friends very much. Highly coloured rumours were
spread about his health. On the Continent, where
Newton's work in optics had made a considerable
impression, and his gravitational work was slowly
penetrating, rumours were spread that he had become
insane, and an interesting story was told to account for
it. It was said that a little dog called Diamond had
caused the loss by fire of Newton's laboratory, together
with a manuscript containing the results of many
years' labours. To add verisimilitude to the narrative
the story went on to say that the meek and mild
Newton " rebuked the author of it with an exclama-
tion, ' O Diamond ! Diamond ! thou little knowest
the mischief done ! ' without adding a single stripe."
We have already seen that Newton did not keep any
domestic animals. The fire, of which so much was
made, and which produced only little damage, took
place much earlier, before Newton had even begun to
write the " Principia."
In 1691 Newton resumed his work on the motions
of the moon. This was a most difficult subject lunar
128 SIR ISAAC NEWTON
theory is even now the most difficult branch of
nervous dynamical astronomy and no doubt Newton's
excitability was aggravated by these head-racking
studies. He desired to get the best possible observa-
tions of the moon in order to verify the results of his
mathematical inquiries, and tried to get into touch
with the Astronomer Royal, Flamsteed. But it was
not till 1694 that really useful information was forth-
coming, and Newton spent much of his time on
his favourite chemical experiments. When Flamsteed
was ready a correspondence ensued between him and
Newton which lasted nearly two years. Flamsteed
gave Newton observations of the moon, as well as the
values he had deduced for the refraction produced by
the air a matter of the greatest importance in con-
nexion with the observations of the exact positions
of heavenly bodies, since the apparent positions are
always affected by the bending of the light rays in
coming from outside the atmosphere into the atmo-
sphere of the earth before reaching our eyes or our
telescopes. Newton was able to make considerable
progress with the theory of both subjects the moon
and refraction and was very grateful indeed. Yet
personal unpleasantness intervened for which Newton
himself must bear a portion of the blame.
Flamsteed was a very peculiar person, a permanent
invalid who was never free from headaches and other
more serious physical affections : he was not treated
at all generously as Astronomer Royal, and had to
pay his way by acting as a vicar at the same time as
doing his astronomical work. He was a religious man
and had an antipathy to Halley who was not very
orthodox in his belief, and who had offended Flamsteed
in astronomical matters. Newton was a very kind
man, but he had gone through considerable physical
suffering and had become impatient and excitable.
He always became irritable in personal matters : in
THE TRANSITIONAL DECADE, 1687-1696 129
the words of his friend Locke : " Newton was a nice *
man to deal with, and a little too apt to raise in him-
self suspicions where there is no ground/' Further,
Newton was a particular friend of Halley's who had
done so much for him.
This triangle led to difficulties and many hard words
were said between Newton and Flamsteed, with Halley
as the provocation. It is sometimes not uninteresting
to note the pettinesses of the great a link is thus
forged between more humble mortals and the men of
transcendent genius, who would otherwise lose all
semblance of frail humanity.
While Newton was thus betraying his human weak-
nesses against the greater weaknesses of Flamsteed, a
complete change in his life and fortunes was preparing
for him. His friend Charles Montague had not been
false to him, but had used the first available oppor-
tunity to give Newton evidence of his friendship, and
at the same time save the reputation of England in
regard to her treatment of the greatest Englishman of
the day. Newton was busy with chemical experiments
once again, and the call that now came to him was
one in which he could exercise to the full his lifelong
interest in metals and alloys.
* Not in the modern sense, but in the Shakespearean sense of
" fussy," " difficile:'
THE GUARDIAN OF THE NATION'S COINAGE,
" Thy silver is become dross."
Isaiah, i, 22
NEWTON had spent thirty-one years as a college
graduate and fellow and university professor.
This was just half of his adult years ; he had
thirty-one years more to live, and these he spent in
the midst of the public affairs of the nation and as
the doyen of British science.
From the time of Queen Elizabeth England had had
a coinage based upon bimetallism both gold and
silver were legal tender. But the silver coinage had
become terribly debased by the use of bad and cheap
alloys as well as by the prevalent habit of clipping
the coins. Things were in a very bad state, even to
the extent of English silver being refused by the Bank
of Amsterdam the then financial centre of Europe.
Such silver coins to the nominal value of five and a
half million pounds sterling were in circulation, the
actual value being less than eighty per cent of the
In 1694 Charles Montague was appointed Chancellor
of the Exchequer, and he decided to restore the silver
coinage to its full value. He had conferences with
various people, including Newton, on the matter.
The House of Lords proposed to cancel all such coins
from some given date, so that the sufferers would be
GUARDIAN OF THE COINAGE, 1696-1727 181
the poorest and those least able to bear it. The House
of Commons decided, however, that the nation had to
bear the loss, and resolved to issue new and full- valued
coins in exchange for the old ones. A vast amount
of work thus fell to the Royal Mint.
Montague was an intimate friend of Newton's and
President of the Royal Society. He therefore realized
that he had in him the right man for carrying through
this difficult project. The Wardenship of the Mint in
London became vacant early in 1696, and on March
i gth of that year Montague wrote to Newton, informing
him that the King had appointed him to this post.
" The office is the most proper for you. . . . Tis
worth five or six hundred pounds per annum, and has
not too much business to require more attendance
than you may spare. I desire you will come up as
soon as you can. ... I believe you may have a
lodging near me." Newton accepted the post, and
took over his new functions without delay.
Although the Wardenship of the Mint had become
a sinecure and incumbents hardly ever " condescended
to come near the Tower," Newton took his new duties
very seriously. Hard work was necessary, as the
debased silver was causing much suffering and foment-
ing popular dissatisfaction. " The ability, the industry
and the strict uprightness of the great philosopher,"
says Macaulay, " speedily produced a complete revolu-
tion throughout the department which was under his
direction." " Well had it been for the publick, had
he acted a few years sooner in that situation," said
one who had business with Newton and could appreci-
ate his merits at first hand.
For three years Newton laboured in the nation's
cause, and in 1699 the recoinage was complete. " Till
the great work was completely done, he resisted firmly,
and almost angrily, every attempt that was made by
men of science, here or on the Continent, to draw him
132 SIR ISAAC NEWTON
away from his official duties." Instead of producing
fifteen thousand pounds' worth of silver per week,
Montague and Newton had been able to increase the
yield to one hundred and twenty thousand pounds'
worth per week. They had to withstand all kinds of
opposition,^ and underhand attempts at bribery and
corruption-^ even open rebellion was threatened in the
country. But a gratified nation recognized its bene-
factors at last. In 1699 Newton was appointed
Master of the Mint, a high office worth between twelve
hundred and fifteen hundred pounds per annum
which he held for the remainder of his life.
Newton enjoyed his new circumstances for one
reason in particular. He was always careless about
money. Although scrupulously exact in all business
matters, he sometimes suffered great losses by fraud
or theft and bore them philosophically. But he took
a great delight in giving money away lavishly. He
was always ready to give, believing that a man should
give during his lifetime and not wait till he is dead.
Newton helped his many relatives, both on the paternal
and on the maternal side : he was particularly kind
to his stepsisters and stepbrother and to their families.
Mary Smith got a permanent allowance from him.
But it was a daughter of Hannah the younger sister
who enjoyed Newton's special favour, and played
a prominent part in his private life.
Hannah Smith had married Robert Barton of
Brigstock, Northamptonshire. In 1679 a daughter
was born, called Catherine. She was a very clever
girl and showed signs of becoming a great beauty.
When Newton went to live in London, Catherine
joined him and kept house for him for many years.
Newton had no official residence at the Mint, although
he apparently lived there in bachelor fashion at first.
In 1697 he took a house in Jermyn Street (also written
German Street), a street running parallel to Piccadilly,
GUARDIAN OF THE COINAGE, 1696-1727 133
and connecting Regent Street and St. James Street.
He had much entertaining to do, and naturally a
beautiful and accomplished young lady, famous for
her conversational powers and ready wit, was just the
person to help Newton with his social duties.
There is a tendency to regard Newton's transfer to
London as a loss to science and as a confession on the
part of the British people that the only way to reward
scientific genius in one of its citizens is to make him
relinquish his scientific work altogether since no
posts exist in the academic sphere that are worth
having, and that may be awarded as prizes for merit
of the highest order. Much may be said even to-day
about the inadequacy of the returns in academic life
in Newton's days they were absurdly inadequate
but it must be pointed out that in Newton's case any
academic reward would by its very nature have been
unsuitable. He was not exhausted scientifically, but he
had made such stupendous scientific discoveries that
he could not hope to improve on them. His place was
no longer in a college or in a laboratory, but rather in
the forefront of his nation's science, putting at the
disposal of his people and of humanity his unique gifts
as a worker and as a thinker.
fFjom 1665 to 1696 Newton was essentially a scientific
researcher, and laboured to unravel the laws of nature.
For an equal period, 1696 to 1727, Newton was the
servant of his nation and the foremost representative
of British learning^ No greater mathematician, physi-
cist and astronomer, combined in one person, ever
existed, no greater Master and Warden of the Mint
ever existed, and no more noble figure could be
imagined to act as the presiding genius over British
science. Newton's place was in Cambridge for the
first half of his adult life, his place was in London
for the second half of his adult life, when he had
performed his scientific mission to mankind, and
134 SIR ISAAC NEWTON
had become a figure of national and international
Although Newton desired to devote himself exclu-
sively to the important task that he had in hand at
the Mint he could not escape being interested in the
scientific problems of the day. He was consulted about
the mathematical syllabus at Christ's Hospital, and
gave excellent advice. He showed his great mathe-
matical ability by solving in a few hours two problems
that the celebrated John Bernoulli put as a challenge
to the greatest mathematicians of the world. One of
these problems had its origin in optical theory, and
deserves mention since it contains the germ of an idea
that has played a fundamental part in dynamical
theory of the last hundred years. The problem was :
Given two points A, B such that the straight line
joining them is neither horizontal nor vertical, to find
how the curve joining them must be drawn, so that if
d particle starts from the top end and falls along the
curve under gravity it shall reach the lower end in the
least possible time. Newton showed that the curve
required is a cycloid, or the path described by a point
on the rim of a wheel while the wheel itself rolls along
the flat ground. Such a curve is called a brachisto-
chrone. The idea underlying the problem is that of
the calculus of variations, and the suggestion that
something in nature, say, a length or a time or an
energy, is a maximum or minimum has become one of
the most fertile methods of dynamical and general
The work on the motions of the moon lay neglected
for a couple of years, but at the end of 1698 Newton
resumed it, once more in conjunction with Flamsteed,
and once more with considerable unpleasantness in
their personal relationships. In 1699, after declining
an offer of a considerable pension from the French
king Newton not only disliked gifts to himself, but
GUARDIAN OF THE COINAGE, 1696-1727 135
he was also a very loyal Whig, " the glory of the Whig
party/ 1 as Macaulay calls him he was elected a
foreign associate of the French Academy, together with
the most celebrated scientists of the day Leibnitz,
James and John Bernoulli, and Roemer.
In 1699 Newton decided that he could not continue
as Lucasian professor, and appointed a deputy in that
remarkable mathematician and theologian, William
Whiston, the translator of Josephus. Whiston was
very unorthodox in religious belief, but with Newton's
help he was elected Lucasian professor, when in 1701
Newton finally resigned his chair and his Trinity
fellowship. As a matter of fact, Whiston was expelled
from Cambridge in 1710 for his heterodox views.
Newton still had a bond of union with Cambridge.
In November, 1701, he was once more elected M.P.
for Cambridge University, and sat till the dissolution
in July, 1702, after the death of King William III, and
the succession to the throne of Queen Anne. Newton
did not seek re-election for some years.
In scientific matters Newton's activity was uninter-
rupted. In 1699 he drew up a scheme for a reformed
calendar, with quite revolutionary suggestions, based
upon an ingenious attempt to correlate the calendar
with the actual equinoxes and solstices. In 1700
Newton sent to Halley a description of an instrument
he had invented for measuring the angle subtended at
the eye by two inaccessible points. The instrument
was, in fact, the sextant, so important in navigation
and surveying: but nobody realized its value, -and
John Hadley reinvented it in 1730 several years after
Newton's death. rTnji7oi Newton published a paper
on scales of temperature, incorporating two discoveries
of great importance. The first was his law of cooling,
which is that the rate of cooling at any moment of a
warm body is proportional to the difference between
the temperature of the body and of the surrounding
136 SIR ISAAC NEWTON
medium, say, air. The second was that while a body
is melting or evaporating its temperature remains
constant. Both discoveries play important roles in
Newton's standing in the world of science was
unchallenged. The great Leibnitz said of him in 1701
that his work in mathematics was worth more than
all that had been done before him. This was an
exaggeration, perhaps, and Leibnitz* relations to
Newton later on did not suggest such a pitch of admira-
tion. In England there was no doubt about Newton's
scientific stature. The Royal Society was the estab-^
lished and recognized repository of all that was best
in English science, and the post of President carried
with it the status of pre-eminence in the world of
knowledge. In November, 1703, Newton was elected
President of the Royal Society. He was at last in the
position, as it were, preordained for him. Most gifted
of all Englishmen, supreme in knowledge and discovery,
standing at the summit of happy achievement, and
enjoying universal approbation and renown, Isaac
Newton had risen from the obscurity of a county
hamlet to be the glory of his nation and a blessing
THE DOYEN OF BRITISH SCIENCE, 1703-1727
Honour is not repugnant to reason, but may arise therefrom.
Baruch Spinoza : " Ethics "
NEWTON had become a prominent national
figure. He moved in the best society and lived
in considerable style. He employed many
servants, kept a carriage, and entertained hospitably
and well. His salary was more than he needed and
he was able to exercise his charitable propensities to
the full. He was ever ready to support the
scholar, and he showed special favour to men in
whom he discerned mathematical ability of a high
The friendship that Newton enjoyed with the House
of Orange was cemented in various ways. When King
William III died in 1702 he was succeeded by his
sister-in-law, Anne, the daughter of ex-King James II.
Her husband was the good-natured Prince George of
Denmark, who was elected to the Royal Society. As
President, Newton came into contact with the Prince
Consort and encouraged him in his design to do some-
thing tangible for science. Prince George offered to
pay the cost of printing Flamsteed's observations,
including his star catalogue, and asked Newton,
together with Wren and several other fellows of the
society, to act as referees in the matter, and to decide
which observations were to be printed and the order
in which they were to be arranged. By the beginning
138 SIR ISAAC NEWTON
of 1705 the referees had reported and the work of
printing could begin.
Queen Anne became interested in these matters, too,
and learnt to see in Newton the man of highest genius
in her land. On April 16, 1705, she visited Cambridge
and held a court at Trinity Lodge . She took advantage
of the occasion to confer upon Newton the dignity of
Yet royal favour carried disappointment in its train.
Parliament had just been dissolved. In the new
elections Newton was prevailed upon by his Cambridge
friends to offer himself for election once more. But
the Tories were in the ascendant, and Newton suffered
ignominious defeat only a month after he had been
dubbed a knight. With four candidates in the field
he was returned bottom of the poll. Newton never
sought parliamentary honours again no real loss to
the nation, since he was not cut out for parliamentary
life or for a political career. He had always been shy
of public discussion, even in matters scientific, and he
never bore with a good grace criticism and opposition.
Of Newton's private life we do not know much. He
seems to have had close friends in other than royal
circles, too, and he is credited with having written a
very oblique sort of proposal of marriage to a Lady
Norris a much-married lady who had survived three
husbands. If the proposal was a reality it had no
serious sequel. Newton was then sixty-three years of
age, and he remained a bachelor to the end of his days.
His niece Catherine continued to keep house for him
till she married.
The most important events in the remainder of
Newton's life were of a scientific nature. Two im-
portant works by nim were published soon after
his elevation to the Presidency of the Royal Society.
The first was on " Optics," and contained a connected
account of all Newton's labours in this subject. The
DOYEN OF BRITISH SCIENCE, 1703-1727 139
manuscript was ready for several years, but Newton
did not wish to have it printed while Hooke lived, as
he did not desire to have any further unpleasantness
with him. Hooke died in 1703 and Newton's " Optics "
was published in 1704.
Unlike the " Principia," the " Optics " was published
in English : a Latin edition appeared in 1706. The
book was a great success : it enjoyed widespread
approval, and several editions both in English and in
Latin were printed within a comparatively few years.
As is to be expected, the book deals with the composite
nature of white light and with the cause of colour in
bodies, with reflection and refraction upon the basis
of Newton's corpuscular view of light, with colours in
thin films and the theory of fits of preference for
reflection and for refraction, with diffraction (called
inflection), with the rainbow, with halos, etc. But
in the first edition of the " Optics " two mathematical
treatises, quite irrelevant to the main purpose of the
book, were added. One was on " Quadratures of
Curves," or really the theory of fluxions as used in
finding areas enclosed by curves : the second was an
account of seventy-two curves of the third order, so-
called cubic curves. If the inclusion of the first paper
was expected to make clear Newton's position as the
inventor of fluxions, then the effect produced was the
very reverse. In the review of the " Optics " in
Leibnitz' organ, the " Acta Eruditorum," written by
Leibnitz himself, but not signed, it was quite broadly
hinted that Newton had simply taken Leibnitz'
published work on the calculus, and rewritten it in
the fluxionary notation !
Newton lectured on algebra while Lucasian professor,
but he had not published his notes on the subject he
was never anxious to display his pure mathematics,
which he looked upon as a tool for physics and astro-
nomy. William Whiston had attended these lectures
140 SIR ISAAC NEWTON
in 1685 and so possessed them in manuscript : he had
them printed in 1707. The book is in Latin and is called
" Universal Arithmetic/' This book, too, was received
with great approval both in England and on the
Continent. An English translation appeared soon,
while a second edition was issued within five years of
Meanwhile, the printing of Flamsteed's observations
went on under Newton's supervision. A first volume was
published in 1707, but the death of the Prince Consort
in 1708, and Flamsteed's own dilatoriness, caused
a delay of several years in the publication of the
remainder. Newton and Flamsteed fell out over this
again and again. The way in which Flamsteed carried
on his work at the Royal Observatory was not con-
sidered satisfactory, and finally the Royal Society asked
the Queen to place the Observatory under some
responsible supervision. At the end of 1710 such a
Board was constituted, with Newton as its chief
member, to examine the instruments at the Observatory
and to put them into proper repair. A violent quarrel
broke out between Newton and Flamsteed- the latter
resenting any interference with his job, in which he
had been working for over thirty years, with only one
hundred pounds per annum to cover salary, instru-
ments, running expenses, etc. Newton lost his temper,
and Flamsteed's subsequent behaviour was almost
vandalistic. The scientific contact between Newton
and Flamsteed did not survive this shock ; they hardly
corresponded again till Flamsteed's death in 1719. In
any case, Newton had obtained sufficient information
about the moon for his purposes namely, a second
edition of the " Principia."
This work had become so scarce that Newton had
more than once been asked by Bentley to allow him
to reissue it. Newton had made a number of notes
in the margin of a copy of the first edition, and in
DOYEN OF BRITISH SCIENCE, 1703-1727 141
June, 1708, he sent this to Bentley, who at once
proceeded with having the work reprinted. But
Bentley became involved in quarrels at Trinity and
Newton was too busy to see to the printing himself.
In the following year a brilliant young mathematician,
Roger Cotes, a fellow of Trinity College, who had been
appointed the first occupant of the Plumian Chair in
astronomy and experimental philosophy at the early
age of twenty-five, was entrusted with the task of
preparing the second edition of the " Principia."
Newton still had some corrections and additions to
make and in October, 1709, Cotes received Newton's
corrected copy through William Whiston. Newton
was busy moving into a new residence in Chelsea when
he had the satisfaction of hearing from Bentley :
" You need not be so shy of giving Mr. Cotes too much
trouble. He has more esteem for you, and obligations
to you, than to think the trouble too grievous ; but,
however, he does it at my orders, to whom he owes
more than that, and so pray you be easy as to that.
We will take care that no little slip in a calculation
shall pass this fine edition. . . ."
The choice of Cotes was a happy one. He set
himself to the task with energy and with insight. He
was not content to " print by the copy sent him," as
Newton had suggested, but to produce a properly
edited work. He consulted with Newton over and
over again as the work of printing went on, and the
long correspondence between Newton and Cotes con-
stitutes one of the most valuable sets of scientific letters
extant. Several additions were incorporated in the
new edition of the " Principia " ; as Newton wrote in
his preface : "In the Third Book the theory of the
moon, and the precession of the equinoxes, are more
fully deduced from their principles, and the theory of
comets is confirmed by several examples, and their
orbits more accurately computed."
142 SIR ISAAC NEWTON
The production of the second edition of the
"Principia" occupied four years (1709-1713). In
1710 Newton changed his residence again, moving to
St. Martin's Street, which runs into Leicester Square.
The house he took was the first one on the left as one
enters the street from the square : it was of some size
and in a suitable position for one who was continually
receiving visits from distinguished Englishmen and
foreigners. His niece, Catherine Barton, had by now
attracted the attention and admiration of numerous
famous men like Dean Swift and Charles Montague
the latter had become Earl of Halifax, and is said to
have wanted to marry her ; but Miss Barton remained
unmarried for some years yet and still served Newton
as the leading figure in his household. Newton himself
was already an old man, nearly seventy years of age.
He was never above middle size, and tended to corpu-
lency as he grew older. He was in good health, but
somewhat clumsy in his attitudes. He was always
friendly, but being continually steeped in meditation
he spoke but little in company. He was by no means
eccentric, but he was as apt to be remiss in his social
duties as negligent of his own comforts. That lie
sometimes sat in bed forgetting to dress himself
through absorption in some problem merely proves
him as human as all of us, not as human, indeed, as
Descartes who, at one period of his life, spent most of
his time in bed. If Newton sometimes thought he
had fed when some kind friend had eaten his lunch
for him, it only proves that he was no slave to food,
just as he had remained free of the serfdom to snuff
In 1711 Newton published an important paper on
mathematical computation, the " Methodus Differen-
tialis," containing formulae that have not lost their
importance to this day. But a storm was brewing
that was soon to break over Newton's head with great
DOYEN OF BRITISH SCIENCE, 1703-1727 143
violence. His negligence with respect to his discovery
of fluxions was bringing its punishment in its train.
As early as 1699 a Swiss mathematician, Facio de
Duillier, had somewhat clumsily broken a lance in
defence of Newton's priority in the discovery of
fluxions. " Compelled by the evidence of facts/' he
said, " I hold Newton to have been the first inventor
of the calculus, and the earliest by several years. And
whether Leibnitz, its second inventor, has borrowed
anything from him, I would prefer to my own judg-
ment that of those who have seen the letters of Newten
and copies of his other manuscripts." When Newton's
" Optics " appeared and the reviewer in the " Acta
Eruditorum" who was, in fact, Leibnitz himself,
under the cloak of anonymity implied that Newton
had plagiarized Leibnitz, the fury of English mathe-
maticians was roused. John Keill of Oxford replied
in 1708, and insinuated quite plainly that Leibnitz
had obtained his differential calculus from some of
Newton's manuscripts to which he had been allowed
access. When Leibnitz read this he sent a strong
protest to the Royal Society and asked that body to
make Keill disown publicly the implied accusation.
Keill did not disown his remarks, but drew attention
to the review in the " Acta Eruditorum," and explained
that from what Leibnitz saw of Newton's letters to
Oldenburg he could discover the idea of the calculus.
Leibnitz was not satisfied, and in December, 1711, he
stated openly that the views expressed by the reviewer
of the " Optics " had been only fair and just.
It was now open war : not only was Keill involved
but the Royal Society and its President, Newton, were
thus dragged into the dispute. It was a very un-
pleasant affair as all disputes involving personalities
must be. Attempts have been made to give deep
motives to the disputants and recondite causes to the
bitterness of feeling evinced. One theory is that
144 SIR ISAAC NEWTON
Leibnitz and Newton were really engaged in a political
quarrel that Newton was a fanatical Tory, and as
such opposed to the Elector of Hanover, so that
Leibnitz naturally also shared in this displeasure.
This pretty theory is, however, inconsistent with
Newton's being " the glory of the Whig party," in the
words of Macaulay, and extraordinarily friendly with
the Elector of Hanover when he became King of
England only a few years later, especially with the
Princess of Wales, who was a particular friend of
Leibnitz. No : it is not necessary to invent such
impossible theories. Newton and Leibnitz were great
men but only men, subject to the passions and failings
of the species.
The Royal Society had to take some action, and in
March, 1712, a committee was appointed to examine
all available documents and to express an opinion as
to the independence and priority of the discovery of
the calculus idea and method by Newton and Leibnitz.
It is a great pity that Newton was himself President
at the time an obvious charge of partiality and
prejudice lay at the door of the committee and would
discount much of the value of its decision. Among
the members were Halley and the mathematicians
Machin, de Moivre and Brook Taylor great names
indeed as well as the Prussian Minister and others.
There can be little doubt that the committee tried to
be as impartial as possible : at the same time it is
clear that it was not an independent jury, but rather
a body appointed to vindicate Newton.
Halley had been many things since Newton had
come to London. Newton helped him to a post in one
of the branch mints. Halley then undertook various
scientific voyages, and finally became Savilian professor
of geometry at Oxford. It was in his handwriting
that the report of the committee was presented. After
giving a brief history of the various papers and letters
DOYEN OF BRITISH SCIENCE, 1703-1727 145
written by Newton the committee reports : " That
the differential method is one and the same with the
method of fluxions, excepting the name and mode of
notation. . . . And therefore we take the proper
question to be, not who invented this or that method,
but who was the first inventor of the method. , . .
For which reasons we reckon Mr. Newton the first
inventor ; and are of opinion that Mr. Keill, in asserting
the same, has been noways injurious to Mr. Leibnitz.
And we submit to the judgment of the Society, whether
the extracts, and letters, and papers, now presented,
together with what is extant to the same purpose, in
Dr. Wallis* third volume, may not deserve to be made
It must be said in all fairness that the committee's
report was a very balanced and reasonable one. Its
suggestion to print the " extracts, letters and papers "
was adopted, and in 1713 there appeared the " Com-
mercium Epistolicum " or Correspondence with John
Collins and others concerning the development of the
method of the calculus.
When Leibnitz heard of this publication he became
furious, and a very acrimonious correspondence ensued,
in which Leibnitz as well as the great John Bernoulli
figured very unsatisfactorily, while Keill, acting no
doubt under Newton's directions, laboured valiantly
in defence and offence. Meanwhile, the second edition
of the " Principia " appeared in 1713, and a second
edition of the " Optics " in 1714. An attempt was
made by Tory intriguers to remove Newton from the
Mint by the offer of a very liberal pension : Newton
declined, and remained in active charge of this institu-
tion. His opinions were sought after on matters
of moment to the country, and when Queen Anne
died in 1714 and was succeeded by the Elector of
Hanover as King George I the " honest blockhead "
who punished so brutally in his cousin-wife the sin
146 SIR ISAAC NEWTON
that he himself practised so flagrantly Newton
remained a favourite at court. The King's son,
George, was declared Prince of Wales ; the Princess
of Wales was the accomplished Caroline of Anspach,
who had regular evenings when distinguished men of
science and learning visited her salon. Needless to
say, Newton was an especially welcome visitor on such
and other occasions.
The weary quarrel over the calculus dragged on.
The new editions of the " Principia " and the " Optics,"
and the succession of the Hanoverian house to the
English throne, suggested to Leibnitz a new weapon
of attack. One of the most important changes in the
second edition of the " Principia " was a general
scholium at the very end of the work. Here Newton
points out very forcibly the inadequacy of the vortex
theory of Descartes, and then proceeds to a semi-
scientific, semi-theological disquisition on the nature
of God, finishing with a slight reference to his ether
theory of gravitation. To the new " Optics," too,
Newton added a number of " queries " containing
views and speculations on the constitution of matter
in its various manifestations, on gravitation, etc.
Leibnitz pounced upon these things as a means of
discrediting his enemy. He had already, in 1710,
attacked Newton's theory of gravitation as introducing
the occult and the miraculous into natural philosophy.
He renewed this attack towards the end of 1715, and
directed his arguments to the Princess of Wales. He
declared that philosophy and natural religion had
decayed among the English, and accused Newton of
materializing the conception of God and limiting His
At the instance of the King, Newton now intervened
personally in the dispute. This led Leibnitz to yet
another attempt to overcome Newton. He challenged
Newton in 1716 to solve a problem which is only
DOYEN OF BRITISH SCIENCE, 1703-1727 147
soluble by a person in complete possession of the ideas
and methods of the calculus. Newton solved the
problem one evening after returning from his duties
at the Mint. The dispute would perhaps have dragged
on indefinitely, but Leibnitz' death in November, 1716,
put a stop to the quarrel in the sense at least that
Leibnitz was silenced and the Englishmen had it all
their own way.
Gottfried Wilhelm Leibnitz was three or four years
younger than Newton. He was a man of remarkable
genius as an administrator, diplomat, philosopher and
mathematician. He was the outstanding German
savant of his day, a man who has left his mark on
metaphysical inquiry and in pure mathematics. His
mathematical genius was for analytical form rather
than for the geometrical and physical intuition in
which Newton excelled. To him the calculus was
more of a mathematical exercise with a beautiful
notation to Newton it was a rugged tool, practical
and penetrating. Newton realized the ideas better,
Leibnitz devised the polished processes.
This makes the dispute all the more regrettable.
The effect of the dispute was to produce an estrange-
ment between the British mathematicians and their
continental colleagues. Newton's successors in England
tried to follow his geometrical methods. They failed
to make any real progress, and the Cambridge school
of mathematics declined and practically died with
Newton. Cambridge became the home of mathe-
matical teaching with an examination tradition that
evolved into the Mathematical Tripos : but it was not
till a century after the end of the Newton-Leibnitz
controversy that Cambridge mathematicians began
to show signs of originality and fertility and this
happened only when the prejudice against the conti-
nental Leibnitzian notation and methods was overcome
and the slavish imitation of Newton abandoned.
148 SIR ISAAC NEWTON
Newton and Leibnitz were independent thinkers
and discoverers. It was Newton's own fault and the
fault of Barrow, Collins and other friends of his youth,
that he was embroiled in controversy over the calculus.
It is a recognized principle that priority is decided by
the date of publication, and not by the date of dis-
covery in the privacy of one's study. This was
acknowledged in Newton's time, too. Nobody denied
to Hadley the merit of and credit for the sextant,
although Newton had invented it thirty years earlier :
Hadley made the discovery public and reaped the
reward. Why should not the prior publication by
Leibnitz have been treated in the same manner ?
Newton had too little respect for his own mathematical
powers, and lived to regret it.
During the progress of the calculus controversy
Newton suffered two severe losses of friends whom he
esteemed highly, Charles Montague, Earl of Halifax,
and Roger Cotes. The former had reached the highest
positions in the State and had done much to re-estab-
lish English finance. He started the National Debt
and the Bank of England, and reformed the currency
with Newton's help. He had been first minister of
the Crown under King William III, and although
forced to retire from much of his public life when the
Tories were the dominant power in the land, he emerged
again as first minister of the Crown under George I.
His death occurred in May, 1715. He had been a
widower for some time some say that he had desired
to marry Newton's niece and he bequeathed one
hundred pounds to Newton as a mark of honour and
esteem, and five thousand pounds with various other
benefits to Catherine Barton " as a token of sincere
love, affection, and esteem I have long had for her
person, and as a small recompense for the pleasure and
happiness I have had in her conversation."
Halifax was only fifty-four years of age when he
DOYEN OF BRITISH SCIENCE, 1703-1727 149
died. Even severer and more tragic was the death of
Roger Cotes in 1716, who was taken away when not
yet thirty-four years old. " If Mr. Cotes had lived,"
Newton said, " we might have known something. 11
Two years after the death of her admirer, Halifax
whether this is significant or not, one cannot say
Catherine Barton, then thirty-eight years of age,
married John Conduitt, a friend of Newton's, nine
years her junior, who enjoyed independent means and
was a member of Parliament. A year later Newton
had the joy of welcoming into the world a grand-niece,
Catherine Conduitt, who later became Viscountess
Lymington and ancestress of the family of the Earl
A semi-domestic event which must have given
Newton much pleasure was the elevation of Halley to
the position of Astronomer Royal in 1720 : no doubt
Newton had a share in making this appointment.
Halley was Secretary of the Royal Society since 1713,
so that Newton had a great source of satisfaction
in the scientific career of this sincere friend and
Newton was now nearly eighty years of age. He
was not frail or obviously aged. We have a portrait
of him at the age of eighty-three, and even then he
looked well a venerable sight with fine silver-white
hair. He never became bald, never wore glasses, and
enjoyed the use of his own teeth to the end. His mind
was lively and alert, and he carried out his official
duties at the Mint and his functions as President of
the Royal Society without interruption. But in 1722
Newton began to suffer from the infirmities of old age.
It \as an affection of the bladder, which turned out
to be much less serious than at first appeared. But
Newton had to take special precautions with his food,
to give up exciting dinner parties, and to give up the
use of his carriage, since jerking motion was liable to
150 SIR ISAAC NEWTON
produce another attack. In this way he remained
tolerably well for about two years.
Newton used this respite for a very important
purpose. A third edition of the " Principia " was
needed. It is remarkable that for each edition of this
great work Newton enjoyed the inestimable advantage
of the printing being carried out under the direct
supervision of a young and energetic man of learning
and talent. Halley was only thirty years of age when
he brought out the first edition in 1687 ; Cotes was
barely thirty-one years of age when he brought out
the second edition in 1713. For the third edition
Newton secured the help of another brilliant young
scientist, Henry Pemberton, who began the task in
1722 when he was twenty-nine years old, and published
the third edition in 1726 when he was barely thirty-
Henry Pemberton was a young doctor who had
become acquainted with the " Principia " when still
a medical student. This made him turn his attention
to mathematical studies, and he became acquainted
with Newton, who recognized in some of Pemberton's
work considerable mathematical power. The old
scientist and the young doctor became great friends
and finally the latter undertook to issue the new edition
of the " Principia. 1 '
Pemberton, like Cotes, was not an editor in the
restricted sense. He discussed with Newton every
point that required consideration during the course of
the printing, and did everything with the knowledge
and approval of his senior. Meanwhile more obvious
signs of physical decay made themselves manifest in
Newton. In August, 1724, he suffered from stone in
the bladder and in January, 1725, he was attacked by
inflammation of the lungs, accompanied by severe
coughing, followed a month later by gout in both feet.
The air of the Leicester Square district was not
DOYEN OF BRITISH SCIENCE, 1703-1727 151
considered good for him, and Newton moved to Orbell's
Buildings, now called Pitt's Buildings, in Pitt Street,
near High Street, Kensington. The change did him
some good, but he felt that he ought to give up his
duties at the Mint. He wanted, apparently, to keep
the Mastership in the family, as he tried to get Conduitt
appointed Master. But this did not materialize, and
Newton remained Master but Conduitt did most of
his work there ! Newton continued to preside at the
Royal Society, but it is on record that he fell asleep
while occupying the chair.
Newton always befriended mathematical genius he
encouraged and helped men like Cotes, Duillier, David
Gregory and Pemberton. In 1725 two Scotch mathe-
maticians received marks of his approval and his kindly
help. Colin Maclaurin was one of the greatest mathe-
maticians that Scotland has produced. In 1717, at
the early age of nineteen, he was appointed professor
of mathematics at the Marischal College, Aberdeen.
But Maclaurin desired to go to Edinburgh, and to
obtain the reversion of the chair held by James Gregory
the nephew of the inventor of the reflecting telescope.
It was Newton's recommendation that in 1725 secured
for Maclaurin the post of assistant and successor to
Gregory, and he even offered to contribute twenty
pounds per annum to the salary of the assistantship
in order to make the arrangement feasible. Maclaurin
became professor a year later.
James Stirling was a brilliant young Oxford student
of mathematics. In 1715, when twenty-three years of
age, he got embroiled with Jacobites and had to flee.
He went to Venice and soon began to publish important
work on geometry. Newton not only got Stirling's
work published in England, but in 1725 obtained
permission for him to return to England. Stirling
had an interesting career in Scotland, finishing off as
the manager of a coal-mine. Newton's approval of
152 SIR ISAAC NEWTON
Maclaurin and Stirling has been more than endorsed
The third edition of the " Principia " was meanwhile
going ahe3d, and early in 1726 it appeared, containing
an excellent portrait of Newton at the age of eighty-
three. Newton's generosity to Pemberton was both
moral and material. He presented him with a sum
of two hundred guineas (he had already given a
hundred guineas to the astronomer Pound, whose
observations Newton used in the new edition) and
paid him a high compliment in the preface. Nobody
ever could complain of Newton as regards personal
generosity. He even remembered to contribute to-
wards the cost of repairing the floor of Colsterworth
The issue of the third edition of the " Principia "
was the end of Newton's scientific work.
THE END, 1727
I do not know what I may appear to the world ; but to myself
I seem to have been only like a boy playing on the sea-shore, and
diverting myself in now and then finding a smoother pebble or a
prettier shell than ordinary, whilst the great ocean of truth lay all
undiscovered before me.
A REMARKABLY useful and well-spent life
was drawing to a close. The great worker and
thinker felt that the end was near. His calm
objectiveness in scientific judgment never deserted
him. Conscious of the unprecedented progress that
he had made in the understanding of Nature's laws, he
was, nevertheless, ever ready to revise his views when
facts seemed to go against them. When, a few months
before his death, he was threatened with the complete
demolition of his structure based on universal gravita-
tion, his reply was simply : " It may be so, there is no
arguing against facts and experiments." Two centuries
have passed and the structure stands firmer than ever.
The last years of Newton's life were occupied with
another interest. The study of chronology is a natural
occupation for a mathematician, and several great
mathematicians have worked at it : the different races
and religions of humanity have seen to it that sufficient
confusion exists to puzzle the most ingenious. Newton
had often read history and chronology as a mental
recreation, and he was induced by the Princess of
Wales to write a brief account of his own views of the
correlation between the dates ipf events in ancient
history. When [Newton found m 1725 that this had
154 SIR ISAAC NEWTON
got into print without his permission, he decided to
prepare a large work on the subject. The " Chronology
of Ancient Kingdoms " was completed only a short
time before his death and was not published till a
year after his death/)
In August, 1726, further physical ailments attacked
Newton. He was confined to his house at Kensington,
and spent much of his time in reading, especially the
Bible. On Tuesday, February 28, 1727, he felt, as he
thought, well enough to go to Crane Court, near Fleet
Street, London to preside at the Royal Society on Thurs-
day, March 2nd. He went, and came back to Kensing-
ton on Saturday, March 4th, seriously ill. This was the
beginning of the end. A week later the illness was
diagnosed as stone in the bladder, and it was felt that
death was near. Newton suffered excruciating pains,
but he bore them patiently and uncomplainingly. In
the intervals he conversed cheerfully, and on Wednes-
day, March I5th, there appeared to be some improve-
ment in his condition. This was an illusion, however.
On Saturday evening, March i8th, he had a relapse
and became insensible. He remained like this till
after midnight of the following day, ano&ied painlessly
between one o'clock and two o'clock in the morning
of Monday, March 20, 1727/1
Newton died in his ei^t^fifth year. The highest
possible posthumous honours were done him. His
body lay in state in the Jerusalem Chamber on Tuesday,
March 28th, and was buried in Westminster Abbey.
A plain flagstone marks the actual grave with the
inscription " Hie depositum est Quod Mortale fuit
Isaaci Newtoni." A monument dedicated to Newton's
memory was erected in 1731, when also a medal was
issued at the Mint in his honour.
Newton left his family estates at Woolsthorpe and
Sewstern to the heir-at-law, the ne'er-do-well, John
Newton, his second cousin. He had already in his
THE END, 1727 155
lifetime made ample provision for more distant relatives
like the Ayscoughs, and for such nearer relations as
were beyond the scope of his bequests by will. His
personal estate of thirty-two thousand pounds went to
his eight living nephews and nieces, the three children
of his stepbrother, Benjamin Smith, the three children of
his stepsister, Mary Pilkington, and the two daughters
of his stepsister, Hannah Barton. The Mastership of
the Mint went to John Conduitt after all.
The impression that Newton made on British
scientific life, and on the scientific life of humanity as
a whole, has remained one of the indelible imprints
on the sands of time. It was only after his death, as
generation after generation of the mightiest intellects
of Europe followed out his ideas, and triumph after
triumph was scored in the elucidation of Nature's
puzzles, that the true greatness of his genius was
appreciated. Rarely, if ever, have so many noble
qualities been united in one man. A great experi-
mentalist and manipulator, a profound mathematician
and theorist, a clear and logical thinker, a fine exponent
and writer, a practical national benefactor, a kind and
appreciative supporter of merit and ability, a model
relation to the members of his family, an example of
unerring rectitude, an abhorrer of all vice and of
cruelty to man and beast Newton has long since
obtained absolution at the hands of posterity for the
faults of temper which sometimes marred his personal
relationships, and the faults of self-appreciation that
ignored the mathematician in himself and sought in-
spiration in the pseudo-science of alchemy. Humanity
will ever rejoice to have counted Newton among its sons.
SlBI GRATULENTUR MORTALES, TALE TANTUMQUE
HUMANI GENERIS DECUS.
Many editions of Newton's chief individual
works, such as the " Principia " and " Optics "
have appeared from time to time, and are easily
obtainable. No really authoritative edition of
his complete works has been issued yet. A col-
lection of Newton's writings in five volumes was
issued by Samuel Horsley in the years 1779-1785,
under the title : Isaaci Newtoni Opera quae
Aberration, chromatic, 59, 60
Academic life, 133
" Acta Eruditorum," 108, 139,
Action at a distance, 122
Alchemy, 125, 155
Algebra, 65, 139
Anne, Queen, 135, 137-8, 145
Apocalypse of St. John, 125
Apple, 45, 46
Apples for cider, 82
Attraction of sphere, no
Authority, 43, 69, 71, 79
Ayscough, 5, 7, 155
Bacon, Roger, 3
Barrow, Isaac, 58, 64-5, 148
Barton, Catherine, 9, 132, 142,
Bentley, Richard, 125-6, 140-1
Bernoulli, James, 135
Bernoulli, John, 134-5, 145
Binomial Theorem, 16-8, 26
Bohr, Niels, 73
Boyle, Robert, 26, 74, 78, 101,
Bradley, James, 77
Brahe, Tycho, n, 38-9, 43, no
Burton Goggles, 7
Byron, Lord, xii
Calendar, 4-5, 135
Cambridge, 16, 123, 138, 147
Caroline of Anspach, Princess of
Wales, 144, 146, 153
Cartesian ovals, 56, 60,
Cassini, Giovanni Domenico, 114
Cavalieri, Bonaventura, 25
Central acceleration, 48-9, 83,
Centre of gravity, 106-7, JI 4
Charles I, i, 2
Charles II, i, 65-6, 71, 90, 92-3
Christ's Hospital, 134
Clark, apothecary, 7
Collins, John, 64-5, 145, 148
Colour, 29, 53, 57-8, 67, 78, 139
Colsterworth, 2, 5, 152
Comets, 9, 88, 90, 93, 117, 119-
Commercium Epistolicum, 145
Conduitt, John, 149, 151, 155
Conduitt, Catherine, Viscountess
Comes, 38-9, 108, 117
Cooling, law of, 135
Copermcan system, 37, 40-1
Copernicus, Nicolas, 10, 35-8, 41,
Corpuscular theory of light, 77,
Cotes, Roger, 141, 149-51
Cromwell, Oliver, 2, 3, 10
Cubic Curves, 139
De Duillier, Facio, 143, 151
Deferent, 32, 35-6
De Moivre, Abraham, 144
De Motu, 91, 94. *7
De Mundi, 96, 107, 112, 117
SIR ISAAC NEWTON
De Revolutionibus Orbium
Descartes, Rene, 16, 42, 56-8,
122, 142, 146
Differential Calculus, 82, 108,
Diffraction, 78, 139
Discs of planets, 37
Dispersion, 59, 68-9
Dispute with Leibnitz, 1437
Earthly and celestial, 33, 38, 93,
Earth, motions of, 35-6, 85, 87
Edinburgh, 123, 151
Einstein, Albert, 73, 119
Ellipse, 39, 40, 83-4, 90, 117,
England, 122, 136
Epicycle, 32, 35-6, 38
Ether, 42, 77-9, 122, 146
Exhaustions, method of, 23
Falling body, 44, 86
Fermat, Pierre de, 25
Fits, 76-8, 139
Fixed stars, 106
Flambteed, John, 88, 93, 101,
114, 128-9, 134, 137, 140
Flattening of earth and planets,
94, in, 114
Fluxions, 19, 21-2, 27, 43, 64,
70, 81-2, 107-8, 125, 139, 143
Foucault, Jean Bernard Leon, 77
French Academy, 135
Fresnel, Augustin Jean, 79
Gale, experiments in, 10
Galilei, Galileo, 37, 42-4, 46, 53,
George, Prince of Denmark,
Prince Consort, 137, 140
George I, Elector of Hanover,
George, Prince of Wales, 146
Grantham, 2, 7, 10, u, 99
Gravitation, 42, 73, 78, 81,
8 3~4. 93, 113, H9> 122, 125,
Greeks, 33, 38
Gregory, David, 151
Gregory, James, 60, 63
Gregory, James (the younger),
Hadley, John, 135, 148
Halos, 53, 139
Halley, Edmund, 89-91, 94-6,
101, 119-21, 123-4, 1-2 8-9,
144, 149, 150
Hero worship, 79
Hcrschel, William, 126
Hooke, Robert, 45, 69, 74, 77-9,
82-4, 86-90, 95-6, 99, 139
Huygens, Christian, 69, 77, 79,
" Hypotheses," 113
Inverse square law, 45, 47, 49,
50, 83-4, 87-8, 90-2, 96, 114
James II, 97, 101, 123, 137
Jeffreys, Judge, 98, 121
Kant, Immanuel, 126
Kcill, John, 143, 145
Kepler, John, n, 25, 38-42, 48,
57, 104, no
Kepler's Laws, 40-1, 48-9, 84,
87, 90, 113
King's College, Cambridge, 124
King's School, Grantham, 2, 7,
Lagrange, Joseph Louis, 118
Laplace, Pierre Simon, 102, 118,
Latent heat, 136
Laws of motion, 42-3, 45, 92,
Leibnitz, Gottfried Wilhelm, 82,
99, 108, 122, 125, 135-6, 139,
Librations of moon, 81, 114
Locke, John, 124, 127, 129
Lucretius, Titus Cams, 126
Macaulay, Lord, 123, 131, 135,
Machm, John, 144
Maclaurin, Colin, 151-2
Market Overton, 5
Mary II, 123
Mathematical Tripos, 147
Mcrcator, Nicolas, 81
Mercury, 48, 119
" Methodus Diff erentialis, " 142
Milton, John, 102
Mint, Royal, 16, 131-3, 151, 155
Monochromatic light, 74
Montague, Charles, Earl of
Halifax, 124, 129-32, 142,
Moon, 30-1, 37, 88, 101, 113,
115-6, 127-8, 134
Moon's distance, 36, 50
Moon's motion, 46, 50-1, 89, 93
Nature, benevolence of, 105, 107,
Nebular hypothesis, 126
Neville's Court, Trinity, 112
Newton, Humphrey, 99
Newton, Isaac :
birth, 2, 4
family, 5, 9, 155
Newton, Isaac (contd.) :
back at school, Miss Storey, n
Trinity College, Cambridge,
12, 15, 19, 62
scientific character, 15, 16, 47,
5*> 77,92, 99, 129, 155
B.A. f 19
plague, 21, 29, 53, 62
falling apple, 45
optics, 60, 62, 66-7, 74-6, 78
gravitation, 60, 81
Fellow of Trinity, 62-3
reflecting telescope, 6j, 65, 67
Lucasian professor, 64-5
Fellow of Royal Society, 66
neglect of food and sleep, 70,
excused holy orders, 71, 92,
excused fees by Royal Society,
Wave-theory of light ; theory
of fits, 76-7
Halley, 90-1, 94
writes "De Motu," 91
" Prmcipia," 94, 101, 122-3,
125, 140-2, 145-6, 150, 152
writes " De Mundi," 96
bachelor life, 98-9, 124, 126
Leibnitz, 82, 122, 143-7
Parliament, 123, 135, 138
Charles Montague, 124, 129 -
32, 142, 148
mother's death, 124
lack of recognition, 124
story of dog Diamond, 127
Warden of Mint, 131
Master of Mint, 132
money matters, 132, 155
residences, 132, 142, 151
SIR ISAAC NEWTON
Newton, Isaac (contd.) :
niece, Catherine Barton, 9,
solves problems, 134, 147
offered pension by French
elected to French Academy,
resigns fellowship and chair,
President of Royal Society,
life in London, 137
knighted by Queen Anne, 138
proposes marriage, 138
Roger Cotes, 141
refuses to retire from Mint,
mathematics, 147, 155
John Conduitt, 149, 151, 155
illnesses, 149, 150
Henry Pemberton, 150-2
on himself, 153
last illness, death, and burial,
Newton, John, heir-at-law, 7,
Newton's rings, 746
Norris, Lady, 138
North Witham, 5
Oldenburg, Henry, 66, 68, 82,
" Optics," 79, 138-9, 143, 145-6
Orthodoxy, Christian, 126
Oscillatory motion, no
Oxford, 1 6, 123, 143-4, 151
Parliament, i, 3, 123, 135, 138
Pemberton, Henry, 150-2
Pendulum, in, 114
Pepys, Samuel, 96, 124
Periodicity in light, 76-7
Perturbations, 109, no, 115
Phases of Venus, 37
Picard, Jean, 84, 89
Plague, Great, 21, 29, 53, 62
Portsmouth family, 149
Precession, 93, in, 114
Principia, 94, 101, 122-3, 125,
140-2, 145-6, 150, 152
Prism, 19, 53, 57-9
Prophecies of Daniel, 125
Ptolemaic system, 31-2
Queries in " Optics," 146
Radius of earth, 50, 52, 84, 89
Rates of change, 22
Reflecting telescope, 53, 60, 63,
65, 67, 83
Refraction, astronomical, 128
Relative motion, 36, 105
Relativity, 73, 119
Resisting medium, in
Roemer, Olaus, 135
Royal Observatory, Greenwich,
13. 92-3, 140
Royal Society, 13, 65-6, 92, 94,
96, 136, 140, 143-4, 149, 151
St. Andrews, 123
Satellites, 37, 93, 113, 115
" Scholia," 107
Sewstern, 5, 71, 154
Sextant, 135, 148
Shakespeare, William, i, 3
Smith, Barnabas, 5
Sound wave, in
Space and time, 103
Spectrum, 53, 67, 73, 139
Stirling, James, 151-2
Stoke Rochford, 7, 45
Storey, Miss, 11
Sun, 30-1, 37, 88, 114, 116
Swift, Dean, 142
Taylor, Brook, 144
Telescope, 53-4, 60, 63, 65-67
Theology, 125-6, 146
Thin films, 74
Tides, 93-4, IIT, 115-6
Transparency and opacity, 78
Turnor, Edmund, 7
Uniform circular motion, 33, 38,
Unity in universe, 49
" Universal Arithmetic," 140
Vortex Theory, 42, 112, 122,
Wallis, John, 25, 108, 125, 145
Wave-theory, 69, 77, 79
Whiston, William, 135, 139, 141
William III, 123, 131, 135, 137
Woolsthorpe, 2, 45, 51, 71, 82-4,
Wren, Christopher, 89, 90, 96,
Young, Thomas, 79
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